Discussion: Should reindex keep the index name if new index has none
As mentioned in #6552 there is an open question about whether reindex should keep the index name if the new index has no name.

Current Behavior:
- reindex keeps index name if the argument is a list or an ndarray
- replaces the index name if the argument is an index, even if the new index does not have a new name.

Related Issues:
#9854
