diff --git a/pandas/tests/frame/methods/test_rename_axis.py b/pandas/tests/frame/methods/test_rename_axis.py
index dd4a77c6509b8..feb83524cc2bb 100644
--- a/pandas/tests/frame/methods/test_rename_axis.py
+++ b/pandas/tests/frame/methods/test_rename_axis.py
@@ -28,6 +28,18 @@ def test_rename_axis_inplace(self, float_frame):
         assert no_return is None
         tm.assert_frame_equal(result, expected)
 
+    def test_rename_axis_with_allows_duplicate_labels_false(self):
+        # GH#44958
+        df = DataFrame([[1, 2], [3, 4]], columns=["a", "b"]).set_flags(
+            allows_duplicate_labels=False
+        )
+
+        result = df.rename_axis("idx", axis=0)
+        expected = DataFrame(
+            [[1, 2], [3, 4]], index=Index([0, 1], name="idx"), columns=["a", "b"]
+        )
+        tm.assert_frame_equal(result, expected, check_flags=False)
+
     def test_rename_axis_raises(self):
         # GH#17833
         df = DataFrame({"A": [1, 2], "B": [1, 2]})
diff --git a/pandas/tests/frame/methods/test_set_axis.py b/pandas/tests/frame/methods/test_set_axis.py
index 7b75bcf4f348d..12f81588e81bf 100644
--- a/pandas/tests/frame/methods/test_set_axis.py
+++ b/pandas/tests/frame/methods/test_set_axis.py
@@ -112,6 +112,16 @@ def obj(self):
         )
         return df
 
+    def test_set_axis_with_allows_duplicate_labels_false(self):
+        # GH#44958
+        df = DataFrame([[1, 2], [3, 4]], columns=["a", "b"]).set_flags(
+            allows_duplicate_labels=False
+        )
+
+        result = df.set_axis(labels=["x", "y"], axis=0)
+        expected = DataFrame([[1, 2], [3, 4]], index=["x", "y"], columns=["a", "b"])
+        tm.assert_frame_equal(result, expected, check_flags=False)
+
 
 class TestSeriesSetAxis(SharedSetAxisTests):
     @pytest.fixture