diff --git a/pandas/tests/frame/methods/test_reset_index.py b/pandas/tests/frame/methods/test_reset_index.py
index a2ab02c5a6038..cd3908fbd5322 100644
--- a/pandas/tests/frame/methods/test_reset_index.py
+++ b/pandas/tests/frame/methods/test_reset_index.py
@@ -772,19 +772,4 @@ def test_errorreset_index_rename(float_frame):
         stacked_df.reset_index(names={"first": "new_first", "second": "new_second"})
 
     with pytest.raises(IndexError, match="list index out of range"):
-        stacked_df.reset_index(names=["new_first"])
-
-
-def test_reset_index_false_index_name():
-    result_series = Series(data=range(5, 10), index=range(0, 5))
-    result_series.index.name = False
-    result_series.reset_index()
-    expected_series = Series(range(5, 10), RangeIndex(range(0, 5), name=False))
-    tm.assert_series_equal(result_series, expected_series)
-
-    # GH 38147
-    result_frame = DataFrame(data=range(5, 10), index=range(0, 5))
-    result_frame.index.name = False
-    result_frame.reset_index()
-    expected_frame = DataFrame(range(5, 10), RangeIndex(range(0, 5), name=False))
-    tm.assert_frame_equal(result_frame, expected_frame)
+        stacked_df.reset_index(names=["new_first"])
\ No newline at end of file