Groupby crash on a single level

pandas/core/groupby/grouper.py

@@ -491,8 +491,14 @@ def get_grouper(
                     raise ValueError("multiple levels only valid with MultiIndex")
 
             if isinstance(level, str):
-                if obj.index.name != level:
-                    raise ValueError(f"level name {level} is not the name of the index")
+                if axis == 0:
+                    axis_name = "index"
+                else:
+                    axis_name = "columns"
+                if getattr(obj, axis_name).name != level:
+                    raise ValueError(
+                        f"level name {level} is not the name of the {axis_name}"
+                    )
             elif level > 0 or level < -1:
                 raise ValueError("level > 0 or level < -1 only valid with MultiIndex")
 

pandas/tests/groupby/test_grouping.py

@@ -511,6 +511,18 @@ def test_groupby_level_index_names(self):
         with pytest.raises(ValueError, match=msg):
             df.groupby(level="foo")
 
+    def test_groupby_level_columns_names(self):
+        # This used to raise with 'level name exp is not the name of the index'
+        df = (
+            DataFrame({"exp": ["A"] * 3 + ["B"] * 3, "var1": range(6)})
+            .set_index("exp")
+            .T
+        )
+        df.groupby(level="exp", axis=1)
+        msg = "level name foo is not the name of the columns"
+        with pytest.raises(ValueError, match=msg):
+            df.groupby(level="foo", axis=1)
+
     @pytest.mark.parametrize("sort", [True, False])
     def test_groupby_level_with_nas(self, sort):
         # GH 17537