@jreback Can you remember the reason that you added the name=self.name in several places in the groupby/rolling/resample refactor? (see 6994240#diff-720d374f1a709d0075a1f0a02445cd65R3376)
I think the fix is correct here, as AFAIU self.name can only be None (and that is already the default for name in Series) or a list (from self._selection) which raises an error as name.

The nested groupy-aplly (e.g. .rolling.groupby.mean does .rolling.groupby.apply(lambda x: mean), and wasn't passing things thru. However the fixing name things was in several places; it may be that this particular change was not needed.

So the path that you are changing is all scalars, so this seems ok. If nothing breaks then you are good to go!.

though the path in the OP is really related to _selection, so this might be a red herring.

In any event I would add a nice comment about why we are not passing name here.

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So the path that you are changing is all scalars, so this seems ok. If nothing breaks then you are good to go!.

Indeed, that was my thought as well

though the path in the OP is really related to _selection, so this might be a red herring.

The problem is that I am not familiar enough to know all use / corner cases of self._selection and self.name. At first sight setting name equal to _selection in case of a selection of multiple columns (so for a DataFrameGroupBy) does not seem to make much sense to me, as you never want to use that as the name of a result

Added a comment

Actually, if I just let name return None instead of _selection (except for SeriesGroupBy, there the property is overwritten), the tests pass as well: jorisvandenbossche@a6f5c9e

lgtm