BUG: In Multilevel.dtypes when level name is not specified it gives wrong output

[gurukiran07]

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• [X] (optional) I have confirmed this bug exists on the master branch of pandas.

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There was a recent PR to add MultiIndex.dtypes #37073 but this only works when each level is named. https://github.com/pandas-dev/pandas/blob/03e1c899077d335a057a3f36c09645499638d417/pandas/core/indexes/multi.py#L703-L710

If level has no name then, level.name would be None.

Example where it fails:

idx_multitype = pd.MultiIndex.from_product(
     [[1, 2, 3], ["a", "b", "c"], pd.date_range("20200101", periods=2, tz="UTC")],
 )
{level.name: level.dtype for level in idx_multitype.levels}
# {None: datetime64[ns, UTC]}

When level is unamed i.e None may be we can add level_0, level_1 etc. this would be consistent with API too(reset_index would add level_x).

@jreback @arw2019

[simonjayhawkins]

Thanks @gurukiran07 for the report. PR to fix welcome.

[gurukiran07]

@simonjayhawkins Made a PR #38582