diff --git a/pandas/tests/indexes/datetimes/test_datetime.py b/pandas/tests/indexes/datetimes/test_datetime.py
index 1776538a15fc2..4a38e3a146c0e 100644
--- a/pandas/tests/indexes/datetimes/test_datetime.py
+++ b/pandas/tests/indexes/datetimes/test_datetime.py
@@ -456,3 +456,15 @@ def test_to_frame_datetime_tz(self):
         result = idx.to_frame()
         expected = DataFrame(idx, index=idx)
         tm.assert_frame_equal(result, expected)
+
+    @pytest.mark.parametrize("name", [None, "name"])
+    def test_index_map(self, name):
+        # see GH20990
+        count = 6
+        index = pd.date_range("2018-01-01", periods=count, freq="M", name=name).map(
+            lambda x: (x.year, x.month)
+        )
+        exp_index = pd.MultiIndex.from_product(
+            ((2018,), range(1, 7)), names=[name, name]
+        )
+        tm.assert_index_equal(index, exp_index)