diff --git a/examples/cluster/plot_kmeans_digits.py b/examples/cluster/plot_kmeans_digits.py
index fc79c867a8589..94bba2a5c52d9 100644
--- a/examples/cluster/plot_kmeans_digits.py
+++ b/examples/cluster/plot_kmeans_digits.py
@@ -114,7 +114,7 @@ def bench_k_means(kmeans, name, data, labels):
 #
 # We will compare three approaches:
 #
-# * an initialization using `kmeans++`. This method is stochastic and we will
+# * an initialization using `k-means++`. This method is stochastic and we will
 #   run the initialization 4 times;
 # * a random initialization. This method is stochastic as well and we will run
 #   the initialization 4 times;
diff --git a/examples/cluster/plot_kmeans_plusplus.py b/examples/cluster/plot_kmeans_plusplus.py
index eea2c2ec85093..1f3507c0062ac 100644
--- a/examples/cluster/plot_kmeans_plusplus.py
+++ b/examples/cluster/plot_kmeans_plusplus.py
@@ -23,7 +23,7 @@
 )
 X = X[:, ::-1]
 
-# Calculate seeds from kmeans++
+# Calculate seeds from k-means++
 centers_init, indices = kmeans_plusplus(X, n_clusters=4, random_state=0)
 
 # Plot init seeds along side sample data
diff --git a/examples/cluster/plot_kmeans_stability_low_dim_dense.py b/examples/cluster/plot_kmeans_stability_low_dim_dense.py
index 774be277037c7..c88cf864506f7 100644
--- a/examples/cluster/plot_kmeans_stability_low_dim_dense.py
+++ b/examples/cluster/plot_kmeans_stability_low_dim_dense.py
@@ -10,7 +10,7 @@
 
 The first plot shows the best inertia reached for each combination
 of the model (``KMeans`` or ``MiniBatchKMeans``), and the init method
-(``init="random"`` or ``init="kmeans++"``) for increasing values of the
+(``init="random"`` or ``init="k-means++"``) for increasing values of the
 ``n_init`` parameter that controls the number of initializations.
 
 The second plot demonstrates one single run of the ``MiniBatchKMeans``
diff --git a/sklearn/cluster/_kmeans.py b/sklearn/cluster/_kmeans.py
index dda68155b47f6..11d2b81cd552f 100644
--- a/sklearn/cluster/_kmeans.py
+++ b/sklearn/cluster/_kmeans.py
@@ -345,7 +345,7 @@ def k_means(
         n_init consecutive runs in terms of inertia.
 
         When `n_init='auto'`, the number of runs depends on the value of init:
-        10 if using `init='random'`, 1 if using `init='kmeans++'`.
+        10 if using `init='random'`, 1 if using `init='k-means++'`.
 
         .. versionadded:: 1.2
            Added 'auto' option for `n_init`.
@@ -1206,7 +1206,7 @@ class KMeans(_BaseKMeans):
         high-dimensional problems (see :ref:`kmeans_sparse_high_dim`).
 
         When `n_init='auto'`, the number of runs depends on the value of init:
-        10 if using `init='random'`, 1 if using `init='kmeans++'`.
+        10 if using `init='random'`, 1 if using `init='k-means++'`.
 
         .. versionadded:: 1.2
            Added 'auto' option for `n_init`.
@@ -1734,7 +1734,7 @@ class MiniBatchKMeans(_BaseKMeans):
         :ref:`kmeans_sparse_high_dim`).
 
         When `n_init='auto'`, the number of runs depends on the value of init:
-        3 if using `init='random'`, 1 if using `init='kmeans++'`.
+        3 if using `init='random'`, 1 if using `init='k-means++'`.
 
         .. versionadded:: 1.2
            Added 'auto' option for `n_init`.