BUG: rolling.cov with multi-index columns should presever the MI (#16825)

xref #16814

Author: jreback

doc/source/whatsnew/v0.20.3.txt

@@ -47,6 +47,7 @@ Bug Fixes
 - Fixed a pytest marker failing downstream packages' tests suites (:issue:`16680`)
 - Bug in reindexing on an empty ``CategoricalIndex`` (:issue:`16770`)
 - Fixed bug where computing the rolling covariance of a MultiIndexed ``DataFrame`` improperly raised a ``ValueError`` (:issue:`16789`)
+- Fixed a bug in failing to compute rolling computations of a column-MultiIndexed ``DataFrame`` (:issue:`16789`, :issue:`16825`)
 
 Conversion
 ^^^^^^^^^^

pandas/tests/indexes/test_multi.py

@@ -61,15 +61,6 @@ def f():
 
         tm.assert_raises_regex(ValueError, 'The truth value of a', f)
 
-    def test_multi_index_names(self):
-
-        # GH 16789
-        cols = pd.MultiIndex.from_product([['A', 'B'], ['C', 'D', 'E']],
-                                          names=['1', '2'])
-        df = pd.DataFrame(np.ones((10, 6)), columns=cols)
-        rolling_result = df.rolling(3).cov()
-        assert rolling_result.index.names == [None, '1', '2']
-
     def test_labels_dtypes(self):
 
         # GH 8456