diff --git a/pandas/tests/frame/test_alter_axes.py b/pandas/tests/frame/test_alter_axes.py
index 4e61c9c62266d..3faf62b4ec28b 100644
--- a/pandas/tests/frame/test_alter_axes.py
+++ b/pandas/tests/frame/test_alter_axes.py
@@ -744,6 +744,15 @@ def test_reset_index(self, float_frame):
         xp = xp.set_index(['B'], append=True)
         tm.assert_frame_equal(rs, xp, check_names=False)
 
+    def test_reset_index_name(self):
+        df = DataFrame([[1, 2, 3, 4], [5, 6, 7, 8]],
+                       columns=['A', 'B', 'C', 'D'],
+                       index=Index(range(2), name='x'))
+        assert df.reset_index().index.name is None
+        assert df.reset_index(drop=True).index.name is None
+        df.reset_index(inplace=True)
+        assert df.index.name is None
+
     def test_reset_index_level(self):
         df = DataFrame([[1, 2, 3, 4], [5, 6, 7, 8]],
                        columns=['A', 'B', 'C', 'D'])
diff --git a/pandas/tests/series/test_alter_axes.py b/pandas/tests/series/test_alter_axes.py
index c3e4cb8bc3abc..7d4aa2d4df6fc 100644
--- a/pandas/tests/series/test_alter_axes.py
+++ b/pandas/tests/series/test_alter_axes.py
@@ -144,6 +144,11 @@ def test_reset_index(self):
         tm.assert_index_equal(rs.index, Index(index.get_level_values(1)))
         assert isinstance(rs, Series)
 
+    def test_reset_index_name(self):
+        s = Series([1, 2, 3], index=Index(range(3), name='x'))
+        assert s.reset_index().index.name is None
+        assert s.reset_index(drop=True).index.name is None
+
     def test_reset_index_level(self):
         df = DataFrame([[1, 2, 3], [4, 5, 6]],
                        columns=['A', 'B', 'C'])
diff --git a/pandas/tests/test_multilevel.py b/pandas/tests/test_multilevel.py
index 0dbbe60283cac..882221bfce4aa 100644
--- a/pandas/tests/test_multilevel.py
+++ b/pandas/tests/test_multilevel.py
@@ -740,13 +740,16 @@ def test_delevel_infer_dtype(self):
     def test_reset_index_with_drop(self):
         deleveled = self.ymd.reset_index(drop=True)
         assert len(deleveled.columns) == len(self.ymd.columns)
+        assert deleveled.index.name == self.ymd.index.name
 
         deleveled = self.series.reset_index()
         assert isinstance(deleveled, DataFrame)
         assert len(deleveled.columns) == len(self.series.index.levels) + 1
+        assert deleveled.index.name == self.series.index.name
 
         deleveled = self.series.reset_index(drop=True)
         assert isinstance(deleveled, Series)
+        assert deleveled.index.name == self.series.index.name
 
     def test_count_level(self):
         def _check_counts(frame, axis=0):