BUG: Cannot map MultiIndex to more levels
- [x] closes #24800 
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

@simonjayhawkins I updated the code to reflect [#24800 (comment)](https://github.com/pandas-dev/pandas/issues/24800#issuecomment-455069121).

Furthermore, I removed the name preservation completely. Keeping the other check,

```python
if self.name:
    names = [self.name] * len(new_values[0])
else:
    names = None
```

would set `names` the first time we switch from an `Index` to a `MultiIndex` but would be lost in successive `map` operations since `MultiIndex` does not set/have a `name` property. Thus, I removed this check as well.

EDIT: There are 5 failing tests which expect a name preservation from `MultiIndex` to `MultiIndex` and one test which expects a name preservation from `Index` to `MultiIndex`. How should this be resolved? > EDIT: There are 5 failing tests which expect a name preservation from `MultiIndex` to `MultiIndex` and one test which expects a name preservation from `Index` to `MultiIndex`. How should this be resolved?

we may need to deprecate the existing behavior. cc @jorisvandenbossche @toobaz  (from #24800 discussion) This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. Thanks for the pull request, but it appears to have gone stale. If interested in continuing, please merge in the main branch, address any review comments and/or failing tests, and we can reopen.