diff --git a/doc/users/next_whats_new/default_filename_suffix.rst b/doc/users/next_whats_new/default_filename_suffix.rst
new file mode 100644
index 000000000000..0f8730b421e0
--- /dev/null
+++ b/doc/users/next_whats_new/default_filename_suffix.rst
@@ -0,0 +1,13 @@
+Stop adding a suffix to suggest unique file name
+------------------------------------------------
+
+Previously, when saving a figure to a file using the GUI's
+save dialog box, if the default filename (based on the
+figure window title) already existed on disk, Matplotlib
+would append a suffix (e.g. `Figure_1-1.png`), preventing
+the dialog from prompting to overwrite the file. This
+behaviour has been removed. Now if the file name exists on
+disk, the user is prompted whether or not to overwrite it.
+This eliminates guesswork, and allows intentional
+overwriting, especially when the figure name has been
+manually set using `fig.canvas.set_window_title()`.
diff --git a/lib/matplotlib/backend_bases.py b/lib/matplotlib/backend_bases.py
index fc92f6dd1869..0000f3416a01 100644
--- a/lib/matplotlib/backend_bases.py
+++ b/lib/matplotlib/backend_bases.py
@@ -2275,17 +2275,6 @@ def get_default_filename(self):
         default_basename = default_basename.replace(' ', '_')
         default_filetype = self.get_default_filetype()
         default_filename = default_basename + '.' + default_filetype
-
-        save_dir = os.path.expanduser(rcParams['savefig.directory'])
-
-        # ensure non-existing filename in save dir
-        i = 1
-        while os.path.isfile(os.path.join(save_dir, default_filename)):
-            # attach numerical count to basename
-            default_filename = (
-                '{}-{}.{}'.format(default_basename, i, default_filetype))
-            i += 1
-
         return default_filename
 
     def switch_backends(self, FigureCanvasClass):
diff --git a/lib/matplotlib/backends/backend_gtk3.py b/lib/matplotlib/backends/backend_gtk3.py
index 0bbab45c0a8b..e5dcb4cbb3aa 100644
--- a/lib/matplotlib/backends/backend_gtk3.py
+++ b/lib/matplotlib/backends/backend_gtk3.py
@@ -592,6 +592,7 @@ def __init__(self,
                 ):
         super().__init__(title, parent, action, buttons)
         self.set_default_response(Gtk.ResponseType.OK)
+        self.set_do_overwrite_confirmation(True)
 
         if not path:
             path = os.getcwd()
diff --git a/lib/matplotlib/tests/test_backend_bases.py b/lib/matplotlib/tests/test_backend_bases.py
index 0ab7e67a7666..3d0142f8996e 100644
--- a/lib/matplotlib/tests/test_backend_bases.py
+++ b/lib/matplotlib/tests/test_backend_bases.py
@@ -60,20 +60,3 @@ def test_get_default_filename():
         assert filename == 'image.png'
     finally:
         shutil.rmtree(test_dir)
-
-
-def test_get_default_filename_already_exists():
-    # From #3068: Suggest non-existing default filename
-    try:
-        test_dir = tempfile.mkdtemp()
-        plt.rcParams['savefig.directory'] = test_dir
-        fig = plt.figure()
-        canvas = FigureCanvasBase(fig)
-
-        # create 'image.png' in figure's save dir
-        open(os.path.join(test_dir, 'image.png'), 'w').close()
-
-        filename = canvas.get_default_filename()
-        assert filename == 'image-1.png'
-    finally:
-        shutil.rmtree(test_dir)