BUG: drop_duplicates drops name(s).
Closes #10115. Closes #10116.

Based on @seth-p  and @jreback 's fix, added tets for datetime-likes.

@jreback could you review this, as this will be the base of #10236 and #10150 (adding `names` to all test cases)
 lgtm. ideally let's try to group tests that work across ALL sub-classes in `test_index`, and leave timeseries specific ones in `tseries/test_base`
 merge when ready
 Thank for review:)
