BUG: Should not raise errors in .set_names for MultiIndex with nlevels == 1 (GH21149)

doc/source/whatsnew/v0.23.1.txt

@@ -80,6 +80,7 @@ Indexing
 
 - Bug in :meth:`Series.reset_index` where appropriate error was not raised with an invalid level name (:issue:`20925`)
 - Bug in :func:`interval_range` when ``start``/``periods`` or ``end``/``periods`` are specified with float ``start`` or ``end`` (:issue:`21161`)
+- Bug in :meth:`MultiIndex.set_names` where error raised for a ``MultiIndex`` with ``nlevels == 1`` (:issue:`21149`)
 -
 
 I/O

pandas/core/indexes/base.py

@@ -1384,7 +1384,8 @@ def set_names(self, names, level=None, inplace=False):
                    names=[u'baz', u'bar'])
         """
 
-        if level is not None and self.nlevels == 1:
+        from .multi import MultiIndex
+        if level is not None and not isinstance(self, MultiIndex):
             raise ValueError('Level must be None for non-MultiIndex')
 
         if level is not None and not is_list_like(level) and is_list_like(

pandas/tests/indexes/test_multi.py

@@ -165,6 +165,22 @@ def test_set_name_methods(self):
         assert res is None
         assert ind.names == new_names2
 
+    @pytest.mark.parametrize('inplace', [True, False])
+    def test_set_names_with_nlevel_1(self, inplace):
+        # GH 21149
+        # Ensure that .set_names for MultiIndex with
+        # nlevels == 1 does not raise any errors
+        expected = pd.MultiIndex(levels=[[0, 1]],
+                                 labels=[[0, 1]],
+                                 names=['first'])
+        m = pd.MultiIndex.from_product([[0, 1]])
+        result = m.set_names('first', level=0, inplace=inplace)
+
+        if inplace:
+            result = m
+
+        tm.assert_index_equal(result, expected)
+
     def test_set_levels_labels_directly(self):
         # setting levels/labels directly raises AttributeError