ENH: Rename index when using DataFrame.reset_index
- [x] closes #6878
- [x] tests added / passed
- [x] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them
- [x] whatsnew entry

Probably the hardest part of this PR is choosing a good name for the new argument. As mentioned in #6878 the `name` keyword is already used in `Series.reset_index`, although to rename the data column. It could be argued that using `name` also in this PR would not cause confusion, since it's hard to assume one can rename a column's name in `DataFrame.reset_index` (which column would it be?). 

Anyway, I've opted for `names`. I've also thought of `rename` but that sounds like asking for a boolean. `new_name` is an option too, although a bit ugly.
> 
> 
> Now I see the problem with that `else` statement, you're absolutely right!
> 
> By the way, could you point me to where the `whatsnew` file is so that I can edit it?

Whatnew file is here: ``doc/source/whatsnew/v1.4.0.rst`` Hello @gcaria! Thanks for updating this PR. We checked the lines you've touched for [PEP 8](https://www.python.org/dev/peps/pep-0008) issues, and found:









There are currently no PEP 8 issues detected in this Pull Request. Cheers! :beers: 

##### Comment last updated at 2021-09-09 11:12:17 UTC This pull request is stale because it has been open for thirty days with no activity. Please update or respond to this comment if you're still interested in working on this. Sorry for the long pause, I've finally added the `Index.get_default_index_names` and `MultiIndex.get_default_index_names` methods, and rebased to master since I was at it. @gcaria - this looks almost there

Please can you get the code-checks passing - see the contributing guide
```
pandas/core/indexes/multi.py:1407:21: PDF005 leading space in concatenated strings
pandas/core/frame.py:5639:89: E501 line too long (94 > 88 characters)
pandas/core/frame.py:5640:89: E501 line too long (89 > 88 characters)
```

Looks like these changes are also causing some test failures - see Azure Pipelines.

`TestResetIndex.test_reset_index_rename_multiindex `

Can you also merge master and address any remaining comments above

Thanks! this was looking good, if you'd merge master and address comments @gcaria - do you still want to work on this? See comment above from Jeff Unfortunately I don't have time to work on this anymore, but all the work is almost done. Thanks for the update. If you happen to find time to work on this PR in the future, or if anyone else wants to finish up this feature, we can reopen. 