BUG: Clean intersection and fix resulting names when MultiIndex are equal
- [x] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`

Names were wrong when MultiIndexes where equal and unique with different names. Additional cleanups

cc @jbrockmendel 
Do not need a whatsnew, cause this was introduced with 7e2aa42c93852bf505c2e34c41ddc8874f04decd PeriodIndex? Missed that. Added it and added a test LGTM cc @jreback > Do not need a whatsnew, cause this was introduced with [7e2aa42](https://github.com/pandas-dev/pandas/commit/7e2aa42c93852bf505c2e34c41ddc8874f04decd)

nope if in the same version (which this is) thanks @phofl 