API: Store name outside attrs
This aligns with xarray and h5py:
https://github.com/pandas-dev/pandas/pull/29062#issuecomment-545703586
sure x- @jbrockmendel comment. @TomAugspurger maybe also add a note somewhere that `attrs` is experimental? When will this feature be not experimental?  Is allows for persistence of data when pickling on accessors.  I would encourage to remove the experimental tag. You can remove the experimental label if you want. The basics aren't go to change. However, there are two future changes that will affect things in attrs

1. `__finalize__` isn't called everywhere: https://github.com/pandas-dev/pandas/issues/31452
2. We might provide an API for merging `.attrs` of multiple dataframes in operations like `concat`. This might be doable in a backwards-compat way. I'm not sure yet.