diff --git a/doc/whats_new/v1.6.rst b/doc/whats_new/v1.6.rst
index 5e44f716812e5..65adb0bbd9004 100644
--- a/doc/whats_new/v1.6.rst
+++ b/doc/whats_new/v1.6.rst
@@ -231,6 +231,11 @@ Changelog
   scoring="max_error" which is now deprecated.
   :pr:`29462` by :user:`Farid "Freddie" Taba <artificialfintelligence>`.
 
+- |API| the `assert_all_finite` parameter of functions
+  :func:`metrics.pairwise.check_pairwise_arrays` and :func:`metrics.pairwise_distances`
+  is renamed into `ensure_all_finite`. `force_all_finite` will be removed in 1.8.
+  :pr:`29404` by :user:`Jérémie du Boisberranger <jeremiedb>`.
+
 :mod:`sklearn.model_selection`
 ..............................
 
@@ -272,6 +277,14 @@ Changelog
   traversed.
   :pr:`27966` by :user:`Adam Li <adam2392>`.
 
+:mod:`sklearn.utils`
+....................
+
+- |API| the `assert_all_finite` parameter of functions :func:`utils.check_array`,
+  :func:`utils.check_X_y`, :func:`utils.as_float_array` is renamed into
+  `ensure_all_finite`. `force_all_finite` will be removed in 1.8.
+  :pr:`29404` by :user:`Jérémie du Boisberranger <jeremiedb>`.
+
 .. rubric:: Code and documentation contributors
 
 Thanks to everyone who has contributed to the maintenance and improvement of
diff --git a/sklearn/cluster/_hdbscan/hdbscan.py b/sklearn/cluster/_hdbscan/hdbscan.py
index 6578f53745f45..58e3febddc652 100644
--- a/sklearn/cluster/_hdbscan/hdbscan.py
+++ b/sklearn/cluster/_hdbscan/hdbscan.py
@@ -737,7 +737,7 @@ def fit(self, X, y=None):
             X = self._validate_data(
                 X,
                 accept_sparse=["csr", "lil"],
-                force_all_finite=False,
+                ensure_all_finite=False,
                 dtype=np.float64,
             )
             self._raw_data = X
@@ -782,7 +782,7 @@ def fit(self, X, y=None):
             # Perform data validation after removing infinite values (numpy.inf)
             # from the given distance matrix.
             X = self._validate_data(
-                X, force_all_finite=False, dtype=np.float64, force_writeable=True
+                X, ensure_all_finite=False, dtype=np.float64, force_writeable=True
             )
             if np.isnan(X).any():
                 # TODO: Support np.nan in Cython implementation for precomputed
diff --git a/sklearn/compose/_column_transformer.py b/sklearn/compose/_column_transformer.py
index c4a3ab67849ea..2f8c28d4b02b9 100644
--- a/sklearn/compose/_column_transformer.py
+++ b/sklearn/compose/_column_transformer.py
@@ -1137,7 +1137,7 @@ def _hstack(self, Xs, *, n_samples):
                 # in a sparse matrix, `check_array` is used for the
                 # dtype conversion if necessary.
                 converted_Xs = [
-                    check_array(X, accept_sparse=True, force_all_finite=False)
+                    check_array(X, accept_sparse=True, ensure_all_finite=False)
                     for X in Xs
                 ]
             except ValueError as e:
@@ -1325,7 +1325,7 @@ def _check_X(X):
     """Use check_array only when necessary, e.g. on lists and other non-array-likes."""
     if hasattr(X, "__array__") or hasattr(X, "__dataframe__") or sparse.issparse(X):
         return X
-    return check_array(X, force_all_finite="allow-nan", dtype=object)
+    return check_array(X, ensure_all_finite="allow-nan", dtype=object)
 
 
 def _is_empty_column_selection(column):
diff --git a/sklearn/compose/_target.py b/sklearn/compose/_target.py
index c2ef2572ab786..476bad9f1e9ed 100644
--- a/sklearn/compose/_target.py
+++ b/sklearn/compose/_target.py
@@ -262,7 +262,7 @@ def fit(self, X, y, **fit_params):
             y,
             input_name="y",
             accept_sparse=False,
-            force_all_finite=True,
+            ensure_all_finite=True,
             ensure_2d=False,
             dtype="numeric",
             allow_nd=True,
diff --git a/sklearn/covariance/_empirical_covariance.py b/sklearn/covariance/_empirical_covariance.py
index 1e194857c64a2..bd2364ab472bb 100644
--- a/sklearn/covariance/_empirical_covariance.py
+++ b/sklearn/covariance/_empirical_covariance.py
@@ -90,7 +90,7 @@ def empirical_covariance(X, *, assume_centered=False):
            [0.25, 0.25, 0.25],
            [0.25, 0.25, 0.25]])
     """
-    X = check_array(X, ensure_2d=False, force_all_finite=False)
+    X = check_array(X, ensure_2d=False, ensure_all_finite=False)
 
     if X.ndim == 1:
         X = np.reshape(X, (1, -1))
diff --git a/sklearn/ensemble/_bagging.py b/sklearn/ensemble/_bagging.py
index 81d3163556626..24bbda275c12d 100644
--- a/sklearn/ensemble/_bagging.py
+++ b/sklearn/ensemble/_bagging.py
@@ -391,7 +391,7 @@ def fit(self, X, y, *, sample_weight=None, **fit_params):
             y,
             accept_sparse=["csr", "csc"],
             dtype=None,
-            force_all_finite=False,
+            ensure_all_finite=False,
             multi_output=True,
         )
 
@@ -941,7 +941,7 @@ def predict_proba(self, X):
             X,
             accept_sparse=["csr", "csc"],
             dtype=None,
-            force_all_finite=False,
+            ensure_all_finite=False,
             reset=False,
         )
 
@@ -991,7 +991,7 @@ def predict_log_proba(self, X):
                 X,
                 accept_sparse=["csr", "csc"],
                 dtype=None,
-                force_all_finite=False,
+                ensure_all_finite=False,
                 reset=False,
             )
 
@@ -1046,7 +1046,7 @@ def decision_function(self, X):
             X,
             accept_sparse=["csr", "csc"],
             dtype=None,
-            force_all_finite=False,
+            ensure_all_finite=False,
             reset=False,
         )
 
@@ -1279,7 +1279,7 @@ def predict(self, X):
             X,
             accept_sparse=["csr", "csc"],
             dtype=None,
-            force_all_finite=False,
+            ensure_all_finite=False,
             reset=False,
         )
 
diff --git a/sklearn/ensemble/_forest.py b/sklearn/ensemble/_forest.py
index d55a0c645e929..cd09c7571a33e 100644
--- a/sklearn/ensemble/_forest.py
+++ b/sklearn/ensemble/_forest.py
@@ -362,7 +362,7 @@ def fit(self, X, y, sample_weight=None):
             multi_output=True,
             accept_sparse="csc",
             dtype=DTYPE,
-            force_all_finite=False,
+            ensure_all_finite=False,
         )
         # _compute_missing_values_in_feature_mask checks if X has missing values and
         # will raise an error if the underlying tree base estimator can't handle missing
@@ -630,16 +630,16 @@ def _validate_X_predict(self, X):
         Validate X whenever one tries to predict, apply, predict_proba."""
         check_is_fitted(self)
         if self.estimators_[0]._support_missing_values(X):
-            force_all_finite = "allow-nan"
+            ensure_all_finite = "allow-nan"
         else:
-            force_all_finite = True
+            ensure_all_finite = True
 
         X = self._validate_data(
             X,
             dtype=DTYPE,
             accept_sparse="csr",
             reset=False,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
         )
         if issparse(X) and (X.indices.dtype != np.intc or X.indptr.dtype != np.intc):
             raise ValueError("No support for np.int64 index based sparse matrices")
diff --git a/sklearn/ensemble/_gb.py b/sklearn/ensemble/_gb.py
index c280ca695bcfd..63792f2c44975 100644
--- a/sklearn/ensemble/_gb.py
+++ b/sklearn/ensemble/_gb.py
@@ -773,7 +773,7 @@ def fit(self, X, y, sample_weight=None, monitor=None):
                 dtype=DTYPE,
                 order="C",
                 accept_sparse="csr",
-                force_all_finite=False,
+                ensure_all_finite=False,
             )
             raw_predictions = self._raw_predict(X_train)
             self._resize_state()
diff --git a/sklearn/ensemble/_hist_gradient_boosting/binning.py b/sklearn/ensemble/_hist_gradient_boosting/binning.py
index ed1bca8558f81..c428c742af883 100644
--- a/sklearn/ensemble/_hist_gradient_boosting/binning.py
+++ b/sklearn/ensemble/_hist_gradient_boosting/binning.py
@@ -194,7 +194,7 @@ def fit(self, X, y=None):
                 )
             )
 
-        X = check_array(X, dtype=[X_DTYPE], force_all_finite=False)
+        X = check_array(X, dtype=[X_DTYPE], ensure_all_finite=False)
         max_bins = self.n_bins - 1
 
         rng = check_random_state(self.random_state)
@@ -275,7 +275,7 @@ def transform(self, X):
         X_binned : array-like of shape (n_samples, n_features)
             The binned data (fortran-aligned).
         """
-        X = check_array(X, dtype=[X_DTYPE], force_all_finite=False)
+        X = check_array(X, dtype=[X_DTYPE], ensure_all_finite=False)
         check_is_fitted(self)
         if X.shape[1] != self.n_bins_non_missing_.shape[0]:
             raise ValueError(
diff --git a/sklearn/ensemble/_hist_gradient_boosting/gradient_boosting.py b/sklearn/ensemble/_hist_gradient_boosting/gradient_boosting.py
index 8db6f7e4d5ff4..c0b79119bfedf 100644
--- a/sklearn/ensemble/_hist_gradient_boosting/gradient_boosting.py
+++ b/sklearn/ensemble/_hist_gradient_boosting/gradient_boosting.py
@@ -263,7 +263,7 @@ def _preprocess_X(self, X, *, reset):
         """
         # If there is a preprocessor, we let the preprocessor handle the validation.
         # Otherwise, we validate the data ourselves.
-        check_X_kwargs = dict(dtype=[X_DTYPE], force_all_finite=False)
+        check_X_kwargs = dict(dtype=[X_DTYPE], ensure_all_finite=False)
         if not reset:
             if self._preprocessor is None:
                 return self._validate_data(X, reset=False, **check_X_kwargs)
diff --git a/sklearn/ensemble/_hist_gradient_boosting/tests/test_compare_lightgbm.py b/sklearn/ensemble/_hist_gradient_boosting/tests/test_compare_lightgbm.py
index bbdcb38ef013a..24b5b02aa0696 100644
--- a/sklearn/ensemble/_hist_gradient_boosting/tests/test_compare_lightgbm.py
+++ b/sklearn/ensemble/_hist_gradient_boosting/tests/test_compare_lightgbm.py
@@ -12,6 +12,10 @@
 from sklearn.model_selection import train_test_split
 
 
+# TODO(1.8) remove the filterwarnings decorator
+@pytest.mark.filterwarnings(
+    "ignore:'force_all_finite' was renamed to 'ensure_all_finite':FutureWarning"
+)
 @pytest.mark.parametrize("seed", range(5))
 @pytest.mark.parametrize(
     "loss",
@@ -118,6 +122,10 @@ def test_same_predictions_regression(
         assert np.mean(np.isclose(pred_lightgbm, pred_sklearn, rtol=1e-4)) > 1 - 0.01
 
 
+# TODO(1.8) remove the filterwarnings decorator
+@pytest.mark.filterwarnings(
+    "ignore:'force_all_finite' was renamed to 'ensure_all_finite':FutureWarning"
+)
 @pytest.mark.parametrize("seed", range(5))
 @pytest.mark.parametrize("min_samples_leaf", (1, 20))
 @pytest.mark.parametrize(
@@ -191,6 +199,10 @@ def test_same_predictions_classification(
         np.testing.assert_almost_equal(acc_lightgbm, acc_sklearn, decimal=2)
 
 
+# TODO(1.8) remove the filterwarnings decorator
+@pytest.mark.filterwarnings(
+    "ignore:'force_all_finite' was renamed to 'ensure_all_finite':FutureWarning"
+)
 @pytest.mark.parametrize("seed", range(5))
 @pytest.mark.parametrize("min_samples_leaf", (1, 20))
 @pytest.mark.parametrize(
diff --git a/sklearn/ensemble/_iforest.py b/sklearn/ensemble/_iforest.py
index b8df148f20a1a..f4694d69e2dbb 100644
--- a/sklearn/ensemble/_iforest.py
+++ b/sklearn/ensemble/_iforest.py
@@ -316,7 +316,7 @@ def fit(self, X, y=None, sample_weight=None):
             Fitted estimator.
         """
         X = self._validate_data(
-            X, accept_sparse=["csc"], dtype=tree_dtype, force_all_finite=False
+            X, accept_sparse=["csc"], dtype=tree_dtype, ensure_all_finite=False
         )
         if issparse(X):
             # Pre-sort indices to avoid that each individual tree of the
@@ -522,7 +522,7 @@ def score_samples(self, X):
             accept_sparse="csr",
             dtype=tree_dtype,
             reset=False,
-            force_all_finite=False,
+            ensure_all_finite=False,
         )
 
         return self._score_samples(X)
diff --git a/sklearn/feature_selection/_base.py b/sklearn/feature_selection/_base.py
index 12553403f4b90..7504f7345a264 100644
--- a/sklearn/feature_selection/_base.py
+++ b/sklearn/feature_selection/_base.py
@@ -103,7 +103,7 @@ def transform(self, X):
             X,
             dtype=None,
             accept_sparse="csr",
-            force_all_finite=not _safe_tags(self, key="allow_nan"),
+            ensure_all_finite=not _safe_tags(self, key="allow_nan"),
             cast_to_ndarray=not preserve_X,
             reset=False,
         )
diff --git a/sklearn/feature_selection/_rfe.py b/sklearn/feature_selection/_rfe.py
index 45b132cf6e460..524c791be6989 100644
--- a/sklearn/feature_selection/_rfe.py
+++ b/sklearn/feature_selection/_rfe.py
@@ -274,7 +274,7 @@ def _fit(self, X, y, step_score=None, **fit_params):
             y,
             accept_sparse="csc",
             ensure_min_features=2,
-            force_all_finite=False,
+            ensure_all_finite=False,
             multi_output=True,
         )
 
@@ -725,7 +725,7 @@ def fit(self, X, y, groups=None):
             y,
             accept_sparse="csr",
             ensure_min_features=2,
-            force_all_finite=False,
+            ensure_all_finite=False,
             multi_output=True,
         )
 
diff --git a/sklearn/feature_selection/_sequential.py b/sklearn/feature_selection/_sequential.py
index 471f9a373a3da..b3216d12f6328 100644
--- a/sklearn/feature_selection/_sequential.py
+++ b/sklearn/feature_selection/_sequential.py
@@ -214,7 +214,7 @@ def fit(self, X, y=None):
             X,
             accept_sparse="csc",
             ensure_min_features=2,
-            force_all_finite=not tags.get("allow_nan", True),
+            ensure_all_finite=not tags.get("allow_nan", True),
         )
         n_features = X.shape[1]
 
diff --git a/sklearn/feature_selection/_variance_threshold.py b/sklearn/feature_selection/_variance_threshold.py
index 7494b72c1acb8..bacce97f1250f 100644
--- a/sklearn/feature_selection/_variance_threshold.py
+++ b/sklearn/feature_selection/_variance_threshold.py
@@ -101,7 +101,7 @@ def fit(self, X, y=None):
             X,
             accept_sparse=("csr", "csc"),
             dtype=np.float64,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
 
         if hasattr(X, "toarray"):  # sparse matrix
diff --git a/sklearn/impute/_base.py b/sklearn/impute/_base.py
index 6109e3fde7b2a..5674bdc5ba85a 100644
--- a/sklearn/impute/_base.py
+++ b/sklearn/impute/_base.py
@@ -323,9 +323,9 @@ def _validate_input(self, X, in_fit):
             dtype = self._fit_dtype
 
         if is_pandas_na(self.missing_values) or is_scalar_nan(self.missing_values):
-            force_all_finite = "allow-nan"
+            ensure_all_finite = "allow-nan"
         else:
-            force_all_finite = True
+            ensure_all_finite = True
 
         try:
             X = self._validate_data(
@@ -334,7 +334,7 @@ def _validate_input(self, X, in_fit):
                 accept_sparse="csc",
                 dtype=dtype,
                 force_writeable=True if not in_fit else None,
-                force_all_finite=force_all_finite,
+                ensure_all_finite=ensure_all_finite,
                 copy=self.copy,
             )
         except ValueError as ve:
@@ -893,15 +893,15 @@ def _get_missing_features_info(self, X):
 
     def _validate_input(self, X, in_fit):
         if not is_scalar_nan(self.missing_values):
-            force_all_finite = True
+            ensure_all_finite = True
         else:
-            force_all_finite = "allow-nan"
+            ensure_all_finite = "allow-nan"
         X = self._validate_data(
             X,
             reset=in_fit,
             accept_sparse=("csc", "csr"),
             dtype=None,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
         )
         _check_inputs_dtype(X, self.missing_values)
         if X.dtype.kind not in ("i", "u", "f", "O"):
diff --git a/sklearn/impute/_iterative.py b/sklearn/impute/_iterative.py
index e2d06844611c9..e753e0d420ed2 100644
--- a/sklearn/impute/_iterative.py
+++ b/sklearn/impute/_iterative.py
@@ -614,16 +614,16 @@ def _initial_imputation(self, X, in_fit=False):
             number of features.
         """
         if is_scalar_nan(self.missing_values):
-            force_all_finite = "allow-nan"
+            ensure_all_finite = "allow-nan"
         else:
-            force_all_finite = True
+            ensure_all_finite = True
 
         X = self._validate_data(
             X,
             dtype=FLOAT_DTYPES,
             order="F",
             reset=in_fit,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
         )
         _check_inputs_dtype(X, self.missing_values)
 
@@ -680,7 +680,7 @@ def _validate_limit(limit, limit_type, n_features):
         limit = limit_bound if limit is None else limit
         if np.isscalar(limit):
             limit = np.full(n_features, limit)
-        limit = check_array(limit, force_all_finite=False, copy=False, ensure_2d=False)
+        limit = check_array(limit, ensure_all_finite=False, copy=False, ensure_2d=False)
         if not limit.shape[0] == n_features:
             raise ValueError(
                 f"'{limit_type}_value' should be of "
diff --git a/sklearn/impute/_knn.py b/sklearn/impute/_knn.py
index 2e18246b4b9bb..f22e1de79cd85 100644
--- a/sklearn/impute/_knn.py
+++ b/sklearn/impute/_knn.py
@@ -225,15 +225,15 @@ def fit(self, X, y=None):
         """
         # Check data integrity and calling arguments
         if not is_scalar_nan(self.missing_values):
-            force_all_finite = True
+            ensure_all_finite = True
         else:
-            force_all_finite = "allow-nan"
+            ensure_all_finite = "allow-nan"
 
         X = self._validate_data(
             X,
             accept_sparse=False,
             dtype=FLOAT_DTYPES,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
             copy=self.copy,
         )
 
@@ -262,15 +262,15 @@ def transform(self, X):
 
         check_is_fitted(self)
         if not is_scalar_nan(self.missing_values):
-            force_all_finite = True
+            ensure_all_finite = True
         else:
-            force_all_finite = "allow-nan"
+            ensure_all_finite = "allow-nan"
         X = self._validate_data(
             X,
             accept_sparse=False,
             dtype=FLOAT_DTYPES,
             force_writeable=True,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
             copy=self.copy,
             reset=False,
         )
@@ -363,7 +363,7 @@ def process_chunk(dist_chunk, start):
             self._fit_X,
             metric=self.metric,
             missing_values=self.missing_values,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
             reduce_func=process_chunk,
         )
         for chunk in gen:
diff --git a/sklearn/inspection/_partial_dependence.py b/sklearn/inspection/_partial_dependence.py
index b74258615a447..913976b2544e3 100644
--- a/sklearn/inspection/_partial_dependence.py
+++ b/sklearn/inspection/_partial_dependence.py
@@ -566,7 +566,7 @@ def partial_dependence(
     # Use check_array only on lists and other non-array-likes / sparse. Do not
     # convert DataFrame into a NumPy array.
     if not (hasattr(X, "__array__") or sparse.issparse(X)):
-        X = check_array(X, force_all_finite="allow-nan", dtype=object)
+        X = check_array(X, ensure_all_finite="allow-nan", dtype=object)
 
     if is_regressor(estimator) and response_method != "auto":
         raise ValueError(
diff --git a/sklearn/inspection/_permutation_importance.py b/sklearn/inspection/_permutation_importance.py
index 8ecd7237b077d..fb3c646a271a6 100644
--- a/sklearn/inspection/_permutation_importance.py
+++ b/sklearn/inspection/_permutation_importance.py
@@ -266,7 +266,7 @@ def permutation_importance(
     array([0.2211..., 0.       , 0.       ])
     """
     if not hasattr(X, "iloc"):
-        X = check_array(X, force_all_finite="allow-nan", dtype=None)
+        X = check_array(X, ensure_all_finite="allow-nan", dtype=None)
 
     # Precompute random seed from the random state to be used
     # to get a fresh independent RandomState instance for each
diff --git a/sklearn/inspection/_plot/partial_dependence.py b/sklearn/inspection/_plot/partial_dependence.py
index ecb421ccdd68a..02abe62dbb2c1 100644
--- a/sklearn/inspection/_plot/partial_dependence.py
+++ b/sklearn/inspection/_plot/partial_dependence.py
@@ -543,7 +543,7 @@ def from_estimator(
         # Use check_array only on lists and other non-array-likes / sparse. Do not
         # convert DataFrame into a NumPy array.
         if not (hasattr(X, "__array__") or sparse.issparse(X)):
-            X = check_array(X, force_all_finite="allow-nan", dtype=object)
+            X = check_array(X, ensure_all_finite="allow-nan", dtype=object)
         n_features = X.shape[1]
 
         feature_names = _check_feature_names(X, feature_names)
diff --git a/sklearn/linear_model/_omp.py b/sklearn/linear_model/_omp.py
index eb4e52be2656c..cf051228d210a 100644
--- a/sklearn/linear_model/_omp.py
+++ b/sklearn/linear_model/_omp.py
@@ -1056,7 +1056,7 @@ def fit(self, X, y, **fit_params):
         _raise_for_params(fit_params, self, "fit")
 
         X, y = self._validate_data(X, y, y_numeric=True, ensure_min_features=2)
-        X = as_float_array(X, copy=False, force_all_finite=False)
+        X = as_float_array(X, copy=False, ensure_all_finite=False)
         cv = check_cv(self.cv, classifier=False)
         if _routing_enabled():
             routed_params = process_routing(self, "fit", **fit_params)
diff --git a/sklearn/linear_model/_ransac.py b/sklearn/linear_model/_ransac.py
index 631a2c1c66815..6943894002c7c 100644
--- a/sklearn/linear_model/_ransac.py
+++ b/sklearn/linear_model/_ransac.py
@@ -363,7 +363,7 @@ def fit(self, X, y, *, sample_weight=None, **fit_params):
         # because that would allow y to be csr. Delay expensive finiteness
         # check to the estimator's own input validation.
         _raise_for_params(fit_params, self, "fit")
-        check_X_params = dict(accept_sparse="csr", force_all_finite=False)
+        check_X_params = dict(accept_sparse="csr", ensure_all_finite=False)
         check_y_params = dict(ensure_2d=False)
         X, y = self._validate_data(
             X, y, validate_separately=(check_X_params, check_y_params)
@@ -630,7 +630,7 @@ def predict(self, X, **params):
         check_is_fitted(self)
         X = self._validate_data(
             X,
-            force_all_finite=False,
+            ensure_all_finite=False,
             accept_sparse=True,
             reset=False,
         )
@@ -678,7 +678,7 @@ def score(self, X, y, **params):
         check_is_fitted(self)
         X = self._validate_data(
             X,
-            force_all_finite=False,
+            ensure_all_finite=False,
             accept_sparse=True,
             reset=False,
         )
diff --git a/sklearn/metrics/pairwise.py b/sklearn/metrics/pairwise.py
index f8b163813d6d6..745767f23e818 100644
--- a/sklearn/metrics/pairwise.py
+++ b/sklearn/metrics/pairwise.py
@@ -42,6 +42,7 @@
     StrOptions,
     validate_params,
 )
+from ..utils.deprecation import _deprecate_force_all_finite
 from ..utils.extmath import row_norms, safe_sparse_dot
 from ..utils.fixes import parse_version, sp_base_version
 from ..utils.parallel import Parallel, delayed
@@ -82,7 +83,8 @@ def check_pairwise_arrays(
     precomputed=False,
     dtype="infer_float",
     accept_sparse="csr",
-    force_all_finite=True,
+    force_all_finite="deprecated",
+    ensure_all_finite=None,
     ensure_2d=True,
     copy=False,
 ):
@@ -138,6 +140,22 @@ def check_pairwise_arrays(
         .. versionchanged:: 0.23
            Accepts `pd.NA` and converts it into `np.nan`.
 
+        .. deprecated:: 1.6
+           `force_all_finite` was renamed to `ensure_all_finite` and will be removed
+           in 1.8.
+
+    ensure_all_finite : bool or 'allow-nan', default=True
+        Whether to raise an error on np.inf, np.nan, pd.NA in array. The
+        possibilities are:
+
+        - True: Force all values of array to be finite.
+        - False: accepts np.inf, np.nan, pd.NA in array.
+        - 'allow-nan': accepts only np.nan and pd.NA values in array. Values
+          cannot be infinite.
+
+        .. versionadded:: 1.6
+           `force_all_finite` was renamed to `ensure_all_finite`.
+
     ensure_2d : bool, default=True
         Whether to raise an error when the input arrays are not 2-dimensional. Setting
         this to `False` is necessary when using a custom metric with certain
@@ -160,6 +178,8 @@ def check_pairwise_arrays(
         An array equal to Y if Y was not None, guaranteed to be a numpy array.
         If Y was None, safe_Y will be a pointer to X.
     """
+    ensure_all_finite = _deprecate_force_all_finite(force_all_finite, ensure_all_finite)
+
     xp, _ = get_namespace(X, Y)
     if any([issparse(X), issparse(Y)]) or _is_numpy_namespace(xp):
         X, Y, dtype_float = _return_float_dtype(X, Y)
@@ -176,7 +196,7 @@ def check_pairwise_arrays(
             accept_sparse=accept_sparse,
             dtype=dtype,
             copy=copy,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
             estimator=estimator,
             ensure_2d=ensure_2d,
         )
@@ -186,7 +206,7 @@ def check_pairwise_arrays(
             accept_sparse=accept_sparse,
             dtype=dtype,
             copy=copy,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
             estimator=estimator,
             ensure_2d=ensure_2d,
         )
@@ -195,7 +215,7 @@ def check_pairwise_arrays(
             accept_sparse=accept_sparse,
             dtype=dtype,
             copy=copy,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
             estimator=estimator,
             ensure_2d=ensure_2d,
         )
@@ -514,9 +534,9 @@ def nan_euclidean_distances(
            [1.41421356]])
     """
 
-    force_all_finite = "allow-nan" if is_scalar_nan(missing_values) else True
+    ensure_all_finite = "allow-nan" if is_scalar_nan(missing_values) else True
     X, Y = check_pairwise_arrays(
-        X, Y, accept_sparse=False, force_all_finite=force_all_finite, copy=copy
+        X, Y, accept_sparse=False, ensure_all_finite=ensure_all_finite, copy=copy
     )
     # Get missing mask for X
     missing_X = _get_mask(X, missing_values)
@@ -1940,13 +1960,13 @@ def _parallel_pairwise(X, Y, func, n_jobs, **kwds):
     return ret
 
 
-def _pairwise_callable(X, Y, metric, force_all_finite=True, **kwds):
+def _pairwise_callable(X, Y, metric, ensure_all_finite=True, **kwds):
     """Handle the callable case for pairwise_{distances,kernels}."""
     X, Y = check_pairwise_arrays(
         X,
         Y,
         dtype=None,
-        force_all_finite=force_all_finite,
+        ensure_all_finite=ensure_all_finite,
         ensure_2d=False,
     )
 
@@ -2221,7 +2241,12 @@ def pairwise_distances_chunked(
         "Y": ["array-like", "sparse matrix", None],
         "metric": [StrOptions(set(_VALID_METRICS) | {"precomputed"}), callable],
         "n_jobs": [Integral, None],
-        "force_all_finite": ["boolean", StrOptions({"allow-nan"})],
+        "force_all_finite": [
+            "boolean",
+            StrOptions({"allow-nan"}),
+            Hidden(StrOptions({"deprecated"})),
+        ],
+        "ensure_all_finite": ["boolean", StrOptions({"allow-nan"}), Hidden(None)],
     },
     prefer_skip_nested_validation=True,
 )
@@ -2231,7 +2256,8 @@ def pairwise_distances(
     metric="euclidean",
     *,
     n_jobs=None,
-    force_all_finite=True,
+    force_all_finite="deprecated",
+    ensure_all_finite=None,
     **kwds,
 ):
     """Compute the distance matrix from a vector array X and optional Y.
@@ -2331,6 +2357,23 @@ def pairwise_distances(
         .. versionchanged:: 0.23
            Accepts `pd.NA` and converts it into `np.nan`.
 
+        .. deprecated:: 1.6
+           `force_all_finite` was renamed to `ensure_all_finite` and will be removed
+           in 1.8.
+
+    ensure_all_finite : bool or 'allow-nan', default=True
+        Whether to raise an error on np.inf, np.nan, pd.NA in array. Ignored
+        for a metric listed in ``pairwise.PAIRWISE_DISTANCE_FUNCTIONS``. The
+        possibilities are:
+
+        - True: Force all values of array to be finite.
+        - False: accepts np.inf, np.nan, pd.NA in array.
+        - 'allow-nan': accepts only np.nan and pd.NA values in array. Values
+          cannot be infinite.
+
+        .. versionadded:: 1.6
+           `force_all_finite` was renamed to `ensure_all_finite`.
+
     **kwds : optional keyword parameters
         Any further parameters are passed directly to the distance function.
         If using a scipy.spatial.distance metric, the parameters are still
@@ -2362,9 +2405,11 @@ def pairwise_distances(
     array([[1., 2.],
            [2., 1.]])
     """
+    ensure_all_finite = _deprecate_force_all_finite(force_all_finite, ensure_all_finite)
+
     if metric == "precomputed":
         X, _ = check_pairwise_arrays(
-            X, Y, precomputed=True, force_all_finite=force_all_finite
+            X, Y, precomputed=True, ensure_all_finite=ensure_all_finite
         )
 
         whom = (
@@ -2379,7 +2424,7 @@ def pairwise_distances(
         func = partial(
             _pairwise_callable,
             metric=metric,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
             **kwds,
         )
     else:
@@ -2393,7 +2438,7 @@ def pairwise_distances(
             warnings.warn(msg, DataConversionWarning)
 
         X, Y = check_pairwise_arrays(
-            X, Y, dtype=dtype, force_all_finite=force_all_finite
+            X, Y, dtype=dtype, ensure_all_finite=ensure_all_finite
         )
 
         # precompute data-derived metric params
diff --git a/sklearn/metrics/tests/test_pairwise.py b/sklearn/metrics/tests/test_pairwise.py
index a1c6d00bed847..b3f8146b275c5 100644
--- a/sklearn/metrics/tests/test_pairwise.py
+++ b/sklearn/metrics/tests/test_pairwise.py
@@ -1637,3 +1637,17 @@ def test_sparse_manhattan_readonly_dataset(csr_container):
     Parallel(n_jobs=2, max_nbytes=0)(
         delayed(manhattan_distances)(m1, m2) for m1, m2 in zip(matrices1, matrices2)
     )
+
+
+# TODO(1.8): remove
+def test_force_all_finite_rename_warning():
+    X = np.random.uniform(size=(10, 10))
+    Y = np.random.uniform(size=(10, 10))
+
+    msg = "'force_all_finite' was renamed to 'ensure_all_finite'"
+
+    with pytest.warns(FutureWarning, match=msg):
+        check_pairwise_arrays(X, Y, force_all_finite=True)
+
+    with pytest.warns(FutureWarning, match=msg):
+        pairwise_distances(X, Y, force_all_finite=True)
diff --git a/sklearn/multiclass.py b/sklearn/multiclass.py
index 0c6252975a7f8..bacbbfd461995 100644
--- a/sklearn/multiclass.py
+++ b/sklearn/multiclass.py
@@ -124,7 +124,7 @@ class _ConstantPredictor(BaseEstimator):
 
     def fit(self, X, y):
         check_params = dict(
-            force_all_finite=False, dtype=None, ensure_2d=False, accept_sparse=True
+            ensure_all_finite=False, dtype=None, ensure_2d=False, accept_sparse=True
         )
         self._validate_data(
             X, y, reset=True, validate_separately=(check_params, check_params)
@@ -136,7 +136,7 @@ def predict(self, X):
         check_is_fitted(self)
         self._validate_data(
             X,
-            force_all_finite=False,
+            ensure_all_finite=False,
             dtype=None,
             accept_sparse=True,
             ensure_2d=False,
@@ -149,7 +149,7 @@ def decision_function(self, X):
         check_is_fitted(self)
         self._validate_data(
             X,
-            force_all_finite=False,
+            ensure_all_finite=False,
             dtype=None,
             accept_sparse=True,
             ensure_2d=False,
@@ -162,7 +162,7 @@ def predict_proba(self, X):
         check_is_fitted(self)
         self._validate_data(
             X,
-            force_all_finite=False,
+            ensure_all_finite=False,
             dtype=None,
             accept_sparse=True,
             ensure_2d=False,
@@ -786,7 +786,7 @@ def fit(self, X, y, **fit_params):
 
         # We need to validate the data because we do a safe_indexing later.
         X, y = self._validate_data(
-            X, y, accept_sparse=["csr", "csc"], force_all_finite=False
+            X, y, accept_sparse=["csr", "csc"], ensure_all_finite=False
         )
         check_classification_targets(y)
 
@@ -889,7 +889,7 @@ def partial_fit(self, X, y, classes=None, **partial_fit_params):
             X,
             y,
             accept_sparse=["csr", "csc"],
-            force_all_finite=False,
+            ensure_all_finite=False,
             reset=first_call,
         )
         check_classification_targets(y)
@@ -962,7 +962,7 @@ def decision_function(self, X):
         X = self._validate_data(
             X,
             accept_sparse=True,
-            force_all_finite=False,
+            ensure_all_finite=False,
             reset=False,
         )
 
diff --git a/sklearn/naive_bayes.py b/sklearn/naive_bayes.py
index e2d5a3dc24de8..f7f9932f590cd 100644
--- a/sklearn/naive_bayes.py
+++ b/sklearn/naive_bayes.py
@@ -1421,14 +1421,14 @@ def _more_tags(self):
     def _check_X(self, X):
         """Validate X, used only in predict* methods."""
         X = self._validate_data(
-            X, dtype="int", accept_sparse=False, force_all_finite=True, reset=False
+            X, dtype="int", accept_sparse=False, ensure_all_finite=True, reset=False
         )
         check_non_negative(X, "CategoricalNB (input X)")
         return X
 
     def _check_X_y(self, X, y, reset=True):
         X, y = self._validate_data(
-            X, y, dtype="int", accept_sparse=False, force_all_finite=True, reset=reset
+            X, y, dtype="int", accept_sparse=False, ensure_all_finite=True, reset=reset
         )
         check_non_negative(X, "CategoricalNB (input X)")
         return X, y
diff --git a/sklearn/preprocessing/_data.py b/sklearn/preprocessing/_data.py
index 68a887f7e2042..62042c6ba831d 100644
--- a/sklearn/preprocessing/_data.py
+++ b/sklearn/preprocessing/_data.py
@@ -218,7 +218,7 @@ def scale(X, *, axis=0, with_mean=True, with_std=True, copy=True):
         ensure_2d=False,
         estimator="the scale function",
         dtype=FLOAT_DTYPES,
-        force_all_finite="allow-nan",
+        ensure_all_finite="allow-nan",
     )
     if sparse.issparse(X):
         if with_mean:
@@ -485,7 +485,7 @@ def partial_fit(self, X, y=None):
             X,
             reset=first_pass,
             dtype=_array_api.supported_float_dtypes(xp),
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
 
         data_min = _array_api._nanmin(X, axis=0, xp=xp)
@@ -530,7 +530,7 @@ def transform(self, X):
             copy=self.copy,
             dtype=_array_api.supported_float_dtypes(xp),
             force_writeable=True,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
             reset=False,
         )
 
@@ -562,7 +562,7 @@ def inverse_transform(self, X):
             copy=self.copy,
             dtype=_array_api.supported_float_dtypes(xp),
             force_writeable=True,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
 
         X -= self.min_
@@ -668,7 +668,11 @@ def minmax_scale(X, feature_range=(0, 1), *, axis=0, copy=True):
     # Unlike the scaler object, this function allows 1d input.
     # If copy is required, it will be done inside the scaler object.
     X = check_array(
-        X, copy=False, ensure_2d=False, dtype=FLOAT_DTYPES, force_all_finite="allow-nan"
+        X,
+        copy=False,
+        ensure_2d=False,
+        dtype=FLOAT_DTYPES,
+        ensure_all_finite="allow-nan",
     )
     original_ndim = X.ndim
 
@@ -909,7 +913,7 @@ def partial_fit(self, X, y=None, sample_weight=None):
             X,
             accept_sparse=("csr", "csc"),
             dtype=FLOAT_DTYPES,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
             reset=first_call,
         )
         n_features = X.shape[1]
@@ -1043,7 +1047,7 @@ def transform(self, X, copy=None):
             copy=copy,
             dtype=FLOAT_DTYPES,
             force_writeable=True,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
 
         if sparse.issparse(X):
@@ -1085,7 +1089,7 @@ def inverse_transform(self, X, copy=None):
             copy=copy,
             dtype=FLOAT_DTYPES,
             force_writeable=True,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
 
         if sparse.issparse(X):
@@ -1247,7 +1251,7 @@ def partial_fit(self, X, y=None):
             reset=first_pass,
             accept_sparse=("csr", "csc"),
             dtype=_array_api.supported_float_dtypes(xp),
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
 
         if sparse.issparse(X):
@@ -1290,7 +1294,7 @@ def transform(self, X):
             reset=False,
             dtype=_array_api.supported_float_dtypes(xp),
             force_writeable=True,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
 
         if sparse.issparse(X):
@@ -1322,7 +1326,7 @@ def inverse_transform(self, X):
             copy=self.copy,
             dtype=_array_api.supported_float_dtypes(xp),
             force_writeable=True,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
 
         if sparse.issparse(X):
@@ -1417,7 +1421,7 @@ def maxabs_scale(X, *, axis=0, copy=True):
         copy=False,
         ensure_2d=False,
         dtype=FLOAT_DTYPES,
-        force_all_finite="allow-nan",
+        ensure_all_finite="allow-nan",
     )
     original_ndim = X.ndim
 
@@ -1592,7 +1596,7 @@ def fit(self, X, y=None):
             X,
             accept_sparse="csc",
             dtype=FLOAT_DTYPES,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
 
         q_min, q_max = self.quantile_range
@@ -1656,7 +1660,7 @@ def transform(self, X):
             dtype=FLOAT_DTYPES,
             force_writeable=True,
             reset=False,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
 
         if sparse.issparse(X):
@@ -1689,7 +1693,7 @@ def inverse_transform(self, X):
             copy=self.copy,
             dtype=FLOAT_DTYPES,
             force_writeable=True,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
 
         if sparse.issparse(X):
@@ -1822,7 +1826,7 @@ def robust_scale(
         copy=False,
         ensure_2d=False,
         dtype=FLOAT_DTYPES,
-        force_all_finite="allow-nan",
+        ensure_all_finite="allow-nan",
     )
     original_ndim = X.ndim
 
@@ -2866,7 +2870,7 @@ def _check_inputs(self, X, in_fit, accept_sparse_negative=False, copy=False):
             # only set force_writeable for the validation at transform time because
             # it's the only place where QuantileTransformer performs inplace operations.
             force_writeable=True if not in_fit else None,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
         # we only accept positive sparse matrix when ignore_implicit_zeros is
         # false and that we call fit or transform.
@@ -3506,7 +3510,7 @@ def _check_input(self, X, in_fit, check_positive=False, check_shape=False):
             dtype=FLOAT_DTYPES,
             force_writeable=True,
             copy=self.copy,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
             reset=in_fit,
         )
 
diff --git a/sklearn/preprocessing/_encoders.py b/sklearn/preprocessing/_encoders.py
index e3924c11fb635..50b3cd9498639 100644
--- a/sklearn/preprocessing/_encoders.py
+++ b/sklearn/preprocessing/_encoders.py
@@ -27,7 +27,7 @@ class _BaseEncoder(TransformerMixin, BaseEstimator):
 
     """
 
-    def _check_X(self, X, force_all_finite=True):
+    def _check_X(self, X, ensure_all_finite=True):
         """
         Perform custom check_array:
         - convert list of strings to object dtype
@@ -41,16 +41,16 @@ def _check_X(self, X, force_all_finite=True):
         """
         if not (hasattr(X, "iloc") and getattr(X, "ndim", 0) == 2):
             # if not a dataframe, do normal check_array validation
-            X_temp = check_array(X, dtype=None, force_all_finite=force_all_finite)
+            X_temp = check_array(X, dtype=None, ensure_all_finite=ensure_all_finite)
             if not hasattr(X, "dtype") and np.issubdtype(X_temp.dtype, np.str_):
-                X = check_array(X, dtype=object, force_all_finite=force_all_finite)
+                X = check_array(X, dtype=object, ensure_all_finite=ensure_all_finite)
             else:
                 X = X_temp
             needs_validation = False
         else:
             # pandas dataframe, do validation later column by column, in order
             # to keep the dtype information to be used in the encoder.
-            needs_validation = force_all_finite
+            needs_validation = ensure_all_finite
 
         n_samples, n_features = X.shape
         X_columns = []
@@ -58,7 +58,7 @@ def _check_X(self, X, force_all_finite=True):
         for i in range(n_features):
             Xi = _safe_indexing(X, indices=i, axis=1)
             Xi = check_array(
-                Xi, ensure_2d=False, dtype=None, force_all_finite=needs_validation
+                Xi, ensure_2d=False, dtype=None, ensure_all_finite=needs_validation
             )
             X_columns.append(Xi)
 
@@ -68,7 +68,7 @@ def _fit(
         self,
         X,
         handle_unknown="error",
-        force_all_finite=True,
+        ensure_all_finite=True,
         return_counts=False,
         return_and_ignore_missing_for_infrequent=False,
     ):
@@ -76,7 +76,7 @@ def _fit(
         self._check_n_features(X, reset=True)
         self._check_feature_names(X, reset=True)
         X_list, n_samples, n_features = self._check_X(
-            X, force_all_finite=force_all_finite
+            X, ensure_all_finite=ensure_all_finite
         )
         self.n_features_in_ = n_features
 
@@ -186,12 +186,12 @@ def _transform(
         self,
         X,
         handle_unknown="error",
-        force_all_finite=True,
+        ensure_all_finite=True,
         warn_on_unknown=False,
         ignore_category_indices=None,
     ):
         X_list, n_samples, n_features = self._check_X(
-            X, force_all_finite=force_all_finite
+            X, ensure_all_finite=ensure_all_finite
         )
         self._check_feature_names(X, reset=False)
         self._check_n_features(X, reset=False)
@@ -975,7 +975,7 @@ def fit(self, X, y=None):
         self._fit(
             X,
             handle_unknown=self.handle_unknown,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
         )
         self._set_drop_idx()
         self._n_features_outs = self._compute_n_features_outs()
@@ -1023,7 +1023,7 @@ def transform(self, X):
         X_int, X_mask = self._transform(
             X,
             handle_unknown=self.handle_unknown,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
             warn_on_unknown=warn_on_unknown,
         )
 
@@ -1495,7 +1495,7 @@ def fit(self, X, y=None):
         fit_results = self._fit(
             X,
             handle_unknown=self.handle_unknown,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
             return_and_ignore_missing_for_infrequent=True,
         )
         self._missing_indices = fit_results["missing_indices"]
@@ -1577,7 +1577,7 @@ def transform(self, X):
         X_int, X_mask = self._transform(
             X,
             handle_unknown=self.handle_unknown,
-            force_all_finite="allow-nan",
+            ensure_all_finite="allow-nan",
             ignore_category_indices=self._missing_indices,
         )
         X_trans = X_int.astype(self.dtype, copy=False)
@@ -1606,7 +1606,7 @@ def inverse_transform(self, X):
             Inverse transformed array.
         """
         check_is_fitted(self)
-        X = check_array(X, force_all_finite="allow-nan")
+        X = check_array(X, ensure_all_finite="allow-nan")
 
         n_samples, _ = X.shape
         n_features = len(self.categories_)
diff --git a/sklearn/preprocessing/_target_encoder.py b/sklearn/preprocessing/_target_encoder.py
index 1855f340c624d..842598daa2dd7 100644
--- a/sklearn/preprocessing/_target_encoder.py
+++ b/sklearn/preprocessing/_target_encoder.py
@@ -325,7 +325,7 @@ def transform(self, X):
             Transformed input.
         """
         X_ordinal, X_known_mask = self._transform(
-            X, handle_unknown="ignore", force_all_finite="allow-nan"
+            X, handle_unknown="ignore", ensure_all_finite="allow-nan"
         )
 
         # If 'multiclass' multiply axis=1 by num of classes else keep shape the same
@@ -356,7 +356,7 @@ def _fit_encodings_all(self, X, y):
         )
 
         check_consistent_length(X, y)
-        self._fit(X, handle_unknown="ignore", force_all_finite="allow-nan")
+        self._fit(X, handle_unknown="ignore", ensure_all_finite="allow-nan")
 
         if self.target_type == "auto":
             accepted_target_types = ("binary", "multiclass", "continuous")
@@ -386,7 +386,7 @@ def _fit_encodings_all(self, X, y):
         self.target_mean_ = np.mean(y, axis=0)
 
         X_ordinal, X_known_mask = self._transform(
-            X, handle_unknown="ignore", force_all_finite="allow-nan"
+            X, handle_unknown="ignore", ensure_all_finite="allow-nan"
         )
         n_categories = np.fromiter(
             (len(category_for_feature) for category_for_feature in self.categories_),
diff --git a/sklearn/semi_supervised/_self_training.py b/sklearn/semi_supervised/_self_training.py
index b1ebea1061e4c..916cf1a338cd2 100644
--- a/sklearn/semi_supervised/_self_training.py
+++ b/sklearn/semi_supervised/_self_training.py
@@ -283,7 +283,7 @@ def fit(self, X, y, **params):
         # we need row slicing support for sparse matrices, but costly finiteness check
         # can be delegated to the base estimator.
         X, y = self._validate_data(
-            X, y, accept_sparse=["csr", "csc", "lil", "dok"], force_all_finite=False
+            X, y, accept_sparse=["csr", "csc", "lil", "dok"], ensure_all_finite=False
         )
 
         if y.dtype.kind in ["U", "S"]:
@@ -415,7 +415,7 @@ def predict(self, X, **params):
         X = self._validate_data(
             X,
             accept_sparse=True,
-            force_all_finite=False,
+            ensure_all_finite=False,
             reset=False,
         )
         return self.estimator_.predict(X, **routed_params.estimator.predict)
@@ -457,7 +457,7 @@ def predict_proba(self, X, **params):
         X = self._validate_data(
             X,
             accept_sparse=True,
-            force_all_finite=False,
+            ensure_all_finite=False,
             reset=False,
         )
         return self.estimator_.predict_proba(X, **routed_params.estimator.predict_proba)
@@ -499,7 +499,7 @@ def decision_function(self, X, **params):
         X = self._validate_data(
             X,
             accept_sparse=True,
-            force_all_finite=False,
+            ensure_all_finite=False,
             reset=False,
         )
         return self.estimator_.decision_function(
@@ -543,7 +543,7 @@ def predict_log_proba(self, X, **params):
         X = self._validate_data(
             X,
             accept_sparse=True,
-            force_all_finite=False,
+            ensure_all_finite=False,
             reset=False,
         )
         return self.estimator_.predict_log_proba(
@@ -589,7 +589,7 @@ def score(self, X, y, **params):
         X = self._validate_data(
             X,
             accept_sparse=True,
-            force_all_finite=False,
+            ensure_all_finite=False,
             reset=False,
         )
         return self.estimator_.score(X, y, **routed_params.estimator.score)
diff --git a/sklearn/tree/_classes.py b/sklearn/tree/_classes.py
index 29352d080414d..efa5eb6e8f84d 100644
--- a/sklearn/tree/_classes.py
+++ b/sklearn/tree/_classes.py
@@ -238,7 +238,7 @@ def _fit(
             # _compute_missing_values_in_feature_mask will check for finite values and
             # compute the missing mask if the tree supports missing values
             check_X_params = dict(
-                dtype=DTYPE, accept_sparse="csc", force_all_finite=False
+                dtype=DTYPE, accept_sparse="csc", ensure_all_finite=False
             )
             check_y_params = dict(ensure_2d=False, dtype=None)
             X, y = self._validate_data(
@@ -475,15 +475,15 @@ def _validate_X_predict(self, X, check_input):
         """Validate the training data on predict (probabilities)."""
         if check_input:
             if self._support_missing_values(X):
-                force_all_finite = "allow-nan"
+                ensure_all_finite = "allow-nan"
             else:
-                force_all_finite = True
+                ensure_all_finite = True
             X = self._validate_data(
                 X,
                 dtype=DTYPE,
                 accept_sparse="csr",
                 reset=False,
-                force_all_finite=force_all_finite,
+                ensure_all_finite=ensure_all_finite,
             )
             if issparse(X) and (
                 X.indices.dtype != np.intc or X.indptr.dtype != np.intc
diff --git a/sklearn/utils/deprecation.py b/sklearn/utils/deprecation.py
index b3eca8053b94a..ff08ec2aceb81 100644
--- a/sklearn/utils/deprecation.py
+++ b/sklearn/utils/deprecation.py
@@ -136,3 +136,28 @@ def _deprecate_Xt_in_inverse_transform(X, Xt):
         return Xt
 
     return X
+
+
+# TODO(1.8): remove force_all_finite and change the default value of ensure_all_finite
+# to True (remove None without deprecation).
+def _deprecate_force_all_finite(force_all_finite, ensure_all_finite):
+    """Helper to deprecate force_all_finite in favor of ensure_all_finite."""
+    if force_all_finite != "deprecated":
+        warnings.warn(
+            "'force_all_finite' was renamed to 'ensure_all_finite' in 1.6 and will be "
+            "removed in 1.8.",
+            FutureWarning,
+        )
+
+        if ensure_all_finite is not None:
+            raise ValueError(
+                "'force_all_finite' and 'ensure_all_finite' cannot be used together. "
+                "Pass `ensure_all_finite` only."
+            )
+
+        return force_all_finite
+
+    if ensure_all_finite is None:
+        return True
+
+    return ensure_all_finite
diff --git a/sklearn/utils/multiclass.py b/sklearn/utils/multiclass.py
index ead7f416368e3..307e4269747b7 100644
--- a/sklearn/utils/multiclass.py
+++ b/sklearn/utils/multiclass.py
@@ -157,7 +157,7 @@ def is_multilabel(y):
         check_y_kwargs = dict(
             accept_sparse=True,
             allow_nd=True,
-            force_all_finite=False,
+            ensure_all_finite=False,
             ensure_2d=False,
             ensure_min_samples=0,
             ensure_min_features=0,
@@ -320,7 +320,7 @@ def type_of_target(y, input_name=""):
     check_y_kwargs = dict(
         accept_sparse=True,
         allow_nd=True,
-        force_all_finite=False,
+        ensure_all_finite=False,
         ensure_2d=False,
         ensure_min_samples=0,
         ensure_min_features=0,
diff --git a/sklearn/utils/tests/test_validation.py b/sklearn/utils/tests/test_validation.py
index 070a47c6700b2..b99dec99498ab 100644
--- a/sklearn/utils/tests/test_validation.py
+++ b/sklearn/utils/tests/test_validation.py
@@ -150,7 +150,7 @@ def test_as_float_array():
 def test_as_float_array_nan(X):
     X[5, 0] = np.nan
     X[6, 1] = np.nan
-    X_converted = as_float_array(X, force_all_finite="allow-nan")
+    X_converted = as_float_array(X, ensure_all_finite="allow-nan")
     assert_allclose_dense_sparse(X_converted, X)
 
 
@@ -198,18 +198,19 @@ def test_ordering():
 
 
 @pytest.mark.parametrize(
-    "value, force_all_finite", [(np.inf, False), (np.nan, "allow-nan"), (np.nan, False)]
+    "value, ensure_all_finite",
+    [(np.inf, False), (np.nan, "allow-nan"), (np.nan, False)],
 )
 @pytest.mark.parametrize("retype", [np.asarray, sp.csr_matrix])
-def test_check_array_force_all_finite_valid(value, force_all_finite, retype):
+def test_check_array_ensure_all_finite_valid(value, ensure_all_finite, retype):
     X = retype(np.arange(4).reshape(2, 2).astype(float))
     X[0, 0] = value
-    X_checked = check_array(X, force_all_finite=force_all_finite, accept_sparse=True)
+    X_checked = check_array(X, ensure_all_finite=ensure_all_finite, accept_sparse=True)
     assert_allclose_dense_sparse(X, X_checked)
 
 
 @pytest.mark.parametrize(
-    "value, input_name, force_all_finite, match_msg",
+    "value, input_name, ensure_all_finite, match_msg",
     [
         (np.inf, "", True, "Input contains infinity"),
         (np.inf, "X", True, "Input X contains infinity"),
@@ -222,14 +223,14 @@ def test_check_array_force_all_finite_valid(value, force_all_finite, retype):
             np.nan,
             "",
             "allow-inf",
-            'force_all_finite should be a bool or "allow-nan"',
+            "ensure_all_finite should be a bool or 'allow-nan'",
         ),
         (np.nan, "", 1, "Input contains NaN"),
     ],
 )
 @pytest.mark.parametrize("retype", [np.asarray, sp.csr_matrix])
-def test_check_array_force_all_finiteinvalid(
-    value, input_name, force_all_finite, match_msg, retype
+def test_check_array_ensure_all_finite_invalid(
+    value, input_name, ensure_all_finite, match_msg, retype
 ):
     X = retype(np.arange(4).reshape(2, 2).astype(np.float64))
     X[0, 0] = value
@@ -237,7 +238,7 @@ def test_check_array_force_all_finiteinvalid(
         check_array(
             X,
             input_name=input_name,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
             accept_sparse=True,
         )
 
@@ -284,17 +285,17 @@ def test_check_array_links_to_imputer_doc_only_for_X(input_name, retype):
         assert extended_msg in ctx.value.args[0]
 
 
-def test_check_array_force_all_finite_object():
+def test_check_array_ensure_all_finite_object():
     X = np.array([["a", "b", np.nan]], dtype=object).T
 
-    X_checked = check_array(X, dtype=None, force_all_finite="allow-nan")
+    X_checked = check_array(X, dtype=None, ensure_all_finite="allow-nan")
     assert X is X_checked
 
-    X_checked = check_array(X, dtype=None, force_all_finite=False)
+    X_checked = check_array(X, dtype=None, ensure_all_finite=False)
     assert X is X_checked
 
     with pytest.raises(ValueError, match="Input contains NaN"):
-        check_array(X, dtype=None, force_all_finite=True)
+        check_array(X, dtype=None, ensure_all_finite=True)
 
 
 @pytest.mark.parametrize(
@@ -315,14 +316,14 @@ def test_check_array_force_all_finite_object():
         (np.array([[1, np.nan]], dtype=object), "cannot convert float NaN to integer"),
     ],
 )
-@pytest.mark.parametrize("force_all_finite", [True, False])
-def test_check_array_force_all_finite_object_unsafe_casting(
-    X, err_msg, force_all_finite
+@pytest.mark.parametrize("ensure_all_finite", [True, False])
+def test_check_array_ensure_all_finite_object_unsafe_casting(
+    X, err_msg, ensure_all_finite
 ):
     # casting a float array containing NaN or inf to int dtype should
-    # raise an error irrespective of the force_all_finite parameter.
+    # raise an error irrespective of the ensure_all_finite parameter.
     with pytest.raises(ValueError, match=err_msg):
-        check_array(X, dtype=int, force_all_finite=force_all_finite)
+        check_array(X, dtype=int, ensure_all_finite=ensure_all_finite)
 
 
 def test_check_array_series_err_msg():
@@ -507,17 +508,17 @@ def test_check_array_pandas_na_support(pd_dtype, dtype, expected_dtype):
     X = pd.DataFrame(X_np, dtype=pd_dtype, columns=["a", "b", "c"])
     # column c has no nans
     X["c"] = X["c"].astype("float")
-    X_checked = check_array(X, force_all_finite="allow-nan", dtype=dtype)
+    X_checked = check_array(X, ensure_all_finite="allow-nan", dtype=dtype)
     assert_allclose(X_checked, X_np)
     assert X_checked.dtype == expected_dtype
 
-    X_checked = check_array(X, force_all_finite=False, dtype=dtype)
+    X_checked = check_array(X, ensure_all_finite=False, dtype=dtype)
     assert_allclose(X_checked, X_np)
     assert X_checked.dtype == expected_dtype
 
     msg = "Input contains NaN"
     with pytest.raises(ValueError, match=msg):
-        check_array(X, force_all_finite=True)
+        check_array(X, ensure_all_finite=True)
 
 
 def test_check_array_panadas_na_support_series():
@@ -528,14 +529,14 @@ def test_check_array_panadas_na_support_series():
 
     msg = "Input contains NaN"
     with pytest.raises(ValueError, match=msg):
-        check_array(X_int64, force_all_finite=True, ensure_2d=False)
+        check_array(X_int64, ensure_all_finite=True, ensure_2d=False)
 
-    X_out = check_array(X_int64, force_all_finite=False, ensure_2d=False)
+    X_out = check_array(X_int64, ensure_all_finite=False, ensure_2d=False)
     assert_allclose(X_out, [1, 2, np.nan])
     assert X_out.dtype == np.float64
 
     X_out = check_array(
-        X_int64, force_all_finite=False, ensure_2d=False, dtype=np.float32
+        X_int64, ensure_all_finite=False, ensure_2d=False, dtype=np.float32
     )
     assert_allclose(X_out, [1, 2, np.nan])
     assert X_out.dtype == np.float32
@@ -1992,7 +1993,7 @@ def test_pandas_array_returns_ndarray(input_values):
         dtype=None,
         ensure_2d=False,
         allow_nd=False,
-        force_all_finite=False,
+        ensure_all_finite=False,
     )
     assert np.issubdtype(result.dtype.kind, np.floating)
     assert_allclose(result, input_values)
@@ -2186,3 +2187,20 @@ def test_check_array_writeable_df():
     # df is backed by a read-only array, a copy is made
     assert not np.may_share_memory(out, df)
     assert out.flags.writeable
+
+
+# TODO(1.8): remove
+def test_force_all_finite_rename_warning():
+    X = np.random.uniform(size=(10, 10))
+    y = np.random.randint(1, size=(10,))
+
+    msg = "'force_all_finite' was renamed to 'ensure_all_finite'"
+
+    with pytest.warns(FutureWarning, match=msg):
+        check_array(X, force_all_finite=True)
+
+    with pytest.warns(FutureWarning, match=msg):
+        check_X_y(X, y, force_all_finite=True)
+
+    with pytest.warns(FutureWarning, match=msg):
+        as_float_array(X, force_all_finite=True)
diff --git a/sklearn/utils/validation.py b/sklearn/utils/validation.py
index af9fdb4a79cba..4bbd922d28e37 100644
--- a/sklearn/utils/validation.py
+++ b/sklearn/utils/validation.py
@@ -18,6 +18,7 @@
 from .. import get_config as _get_config
 from ..exceptions import DataConversionWarning, NotFittedError, PositiveSpectrumWarning
 from ..utils._array_api import _asarray_with_order, _is_numpy_namespace, get_namespace
+from ..utils.deprecation import _deprecate_force_all_finite
 from ..utils.fixes import ComplexWarning, _preserve_dia_indices_dtype
 from ._isfinite import FiniteStatus, cy_isfinite
 from .fixes import _object_dtype_isnan
@@ -212,7 +213,9 @@ def assert_all_finite(
     )
 
 
-def as_float_array(X, *, copy=True, force_all_finite=True):
+def as_float_array(
+    X, *, copy=True, force_all_finite="deprecated", ensure_all_finite=None
+):
     """Convert an array-like to an array of floats.
 
     The new dtype will be np.float32 or np.float64, depending on the original
@@ -243,6 +246,22 @@ def as_float_array(X, *, copy=True, force_all_finite=True):
         .. versionchanged:: 0.23
            Accepts `pd.NA` and converts it into `np.nan`
 
+        .. deprecated:: 1.6
+           `force_all_finite` was renamed to `ensure_all_finite` and will be removed
+           in 1.8.
+
+    ensure_all_finite : bool or 'allow-nan', default=True
+        Whether to raise an error on np.inf, np.nan, pd.NA in X. The
+        possibilities are:
+
+        - True: Force all values of X to be finite.
+        - False: accepts np.inf, np.nan, pd.NA in X.
+        - 'allow-nan': accepts only np.nan and pd.NA values in X. Values cannot
+          be infinite.
+
+        .. versionadded:: 1.6
+           `force_all_finite` was renamed to `ensure_all_finite`.
+
     Returns
     -------
     XT : {ndarray, sparse matrix}
@@ -256,6 +275,8 @@ def as_float_array(X, *, copy=True, force_all_finite=True):
     >>> as_float_array(array)
     array([0., 0., 1., 2., 2.])
     """
+    ensure_all_finite = _deprecate_force_all_finite(force_all_finite, ensure_all_finite)
+
     if isinstance(X, np.matrix) or (
         not isinstance(X, np.ndarray) and not sp.issparse(X)
     ):
@@ -264,7 +285,7 @@ def as_float_array(X, *, copy=True, force_all_finite=True):
             accept_sparse=["csr", "csc", "coo"],
             dtype=np.float64,
             copy=copy,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
             ensure_2d=False,
         )
     elif sp.issparse(X) and X.dtype in [np.float32, np.float64]:
@@ -514,7 +535,7 @@ def _ensure_sparse_format(
     accept_sparse,
     dtype,
     copy,
-    force_all_finite,
+    ensure_all_finite,
     accept_large_sparse,
     estimator_name=None,
     input_name="",
@@ -542,7 +563,7 @@ def _ensure_sparse_format(
         Whether a forced copy will be triggered. If copy=False, a copy might
         be triggered by a conversion.
 
-    force_all_finite : bool or 'allow-nan'
+    ensure_all_finite : bool or 'allow-nan'
         Whether to raise an error on np.inf, np.nan, pd.NA in X. The
         possibilities are:
 
@@ -552,7 +573,7 @@ def _ensure_sparse_format(
           be infinite.
 
         .. versionadded:: 0.20
-           ``force_all_finite`` accepts the string ``'allow-nan'``.
+           ``ensure_all_finite`` accepts the string ``'allow-nan'``.
 
         .. versionchanged:: 0.23
            Accepts `pd.NA` and converts it into `np.nan`
@@ -615,7 +636,7 @@ def _ensure_sparse_format(
         # force copy
         sparse_container = sparse_container.copy()
 
-    if force_all_finite:
+    if ensure_all_finite:
         if not hasattr(sparse_container, "data"):
             warnings.warn(
                 f"Can't check {sparse_container.format} sparse matrix for nan or inf.",
@@ -624,7 +645,7 @@ def _ensure_sparse_format(
         else:
             _assert_all_finite(
                 sparse_container.data,
-                allow_nan=force_all_finite == "allow-nan",
+                allow_nan=ensure_all_finite == "allow-nan",
                 estimator_name=estimator_name,
                 input_name=input_name,
             )
@@ -718,7 +739,8 @@ def check_array(
     order=None,
     copy=False,
     force_writeable=False,
-    force_all_finite=True,
+    force_all_finite="deprecated",
+    ensure_all_finite=None,
     ensure_2d=True,
     allow_nd=False,
     ensure_min_samples=1,
@@ -790,6 +812,22 @@ def check_array(
         .. versionchanged:: 0.23
            Accepts `pd.NA` and converts it into `np.nan`
 
+        .. deprecated:: 1.6
+           `force_all_finite` was renamed to `ensure_all_finite` and will be removed
+           in 1.8.
+
+    ensure_all_finite : bool or 'allow-nan', default=True
+        Whether to raise an error on np.inf, np.nan, pd.NA in array. The
+        possibilities are:
+
+        - True: Force all values of array to be finite.
+        - False: accepts np.inf, np.nan, pd.NA in array.
+        - 'allow-nan': accepts only np.nan and pd.NA values in array. Values
+          cannot be infinite.
+
+        .. versionadded:: 1.6
+           `force_all_finite` was renamed to `ensure_all_finite`.
+
     ensure_2d : bool, default=True
         Whether to raise a value error if array is not 2D.
 
@@ -831,6 +869,8 @@ def check_array(
     >>> X_checked
     array([[1, 2, 3], [4, 5, 6]])
     """
+    ensure_all_finite = _deprecate_force_all_finite(force_all_finite, ensure_all_finite)
+
     if isinstance(array, np.matrix):
         raise TypeError(
             "np.matrix is not supported. Please convert to a numpy array with "
@@ -924,11 +964,10 @@ def is_sparse(dtype):
         # Since we converted here, we do not need to convert again later
         dtype = None
 
-    if force_all_finite not in (True, False, "allow-nan"):
+    if ensure_all_finite not in (True, False, "allow-nan"):
         raise ValueError(
-            'force_all_finite should be a bool or "allow-nan". Got {!r} instead'.format(
-                force_all_finite
-            )
+            "ensure_all_finite should be a bool or 'allow-nan'. Got "
+            f"{ensure_all_finite!r} instead."
         )
 
     if dtype is not None and _is_numpy_namespace(xp):
@@ -967,7 +1006,7 @@ def is_sparse(dtype):
             accept_sparse=accept_sparse,
             dtype=dtype,
             copy=copy,
-            force_all_finite=force_all_finite,
+            ensure_all_finite=ensure_all_finite,
             accept_large_sparse=accept_large_sparse,
             estimator_name=estimator_name,
             input_name=input_name,
@@ -1054,12 +1093,12 @@ def is_sparse(dtype):
                 % (array.ndim, estimator_name)
             )
 
-        if force_all_finite:
+        if ensure_all_finite:
             _assert_all_finite(
                 array,
                 input_name=input_name,
                 estimator_name=estimator_name,
-                allow_nan=force_all_finite == "allow-nan",
+                allow_nan=ensure_all_finite == "allow-nan",
             )
 
         if copy:
@@ -1155,7 +1194,8 @@ def check_X_y(
     order=None,
     copy=False,
     force_writeable=False,
-    force_all_finite=True,
+    force_all_finite="deprecated",
+    ensure_all_finite=None,
     ensure_2d=True,
     allow_nd=False,
     multi_output=False,
@@ -1217,7 +1257,7 @@ def check_X_y(
         .. versionadded:: 1.6
 
     force_all_finite : bool or 'allow-nan', default=True
-        Whether to raise an error on np.inf, np.nan, pd.NA in X. This parameter
+        Whether to raise an error on np.inf, np.nan, pd.NA in array. This parameter
         does not influence whether y can have np.inf, np.nan, pd.NA values.
         The possibilities are:
 
@@ -1232,6 +1272,23 @@ def check_X_y(
         .. versionchanged:: 0.23
            Accepts `pd.NA` and converts it into `np.nan`
 
+        .. deprecated:: 1.6
+           `force_all_finite` was renamed to `ensure_all_finite` and will be removed
+           in 1.8.
+
+    ensure_all_finite : bool or 'allow-nan', default=True
+        Whether to raise an error on np.inf, np.nan, pd.NA in array. This parameter
+        does not influence whether y can have np.inf, np.nan, pd.NA values.
+        The possibilities are:
+
+        - True: Force all values of X to be finite.
+        - False: accepts np.inf, np.nan, pd.NA in X.
+        - 'allow-nan': accepts only np.nan or pd.NA values in X. Values cannot
+          be infinite.
+
+        .. versionadded:: 1.6
+           `force_all_finite` was renamed to `ensure_all_finite`.
+
     ensure_2d : bool, default=True
         Whether to raise a value error if X is not 2D.
 
@@ -1292,6 +1349,8 @@ def check_X_y(
             f"{estimator_name} requires y to be passed, but the target y is None"
         )
 
+    ensure_all_finite = _deprecate_force_all_finite(force_all_finite, ensure_all_finite)
+
     X = check_array(
         X,
         accept_sparse=accept_sparse,
@@ -1300,7 +1359,7 @@ def check_X_y(
         order=order,
         copy=copy,
         force_writeable=force_writeable,
-        force_all_finite=force_all_finite,
+        ensure_all_finite=ensure_all_finite,
         ensure_2d=ensure_2d,
         allow_nd=allow_nd,
         ensure_min_samples=ensure_min_samples,
@@ -1322,7 +1381,7 @@ def _check_y(y, multi_output=False, y_numeric=False, estimator=None):
         y = check_array(
             y,
             accept_sparse="csr",
-            force_all_finite=True,
+            ensure_all_finite=True,
             ensure_2d=False,
             dtype=None,
             input_name="y",
@@ -1377,7 +1436,7 @@ def column_or_1d(y, *, dtype=None, warn=False):
         ensure_2d=False,
         dtype=dtype,
         input_name="y",
-        force_all_finite=False,
+        ensure_all_finite=False,
         ensure_min_samples=0,
     )