Add invariant check for IndexVariable.name

[dcherian]

@benbovy this seems to be the root cause of #8646, the variable name in Dataset._variables does not match IndexVariable.name.

A good number of tests seem to fail though, so not sure if this is a good chck.

• Closes #xxxx
• Tests added
• User visible changes (including notable bug fixes) are documented in whats-new.rst
• New functions/methods are listed in api.rst

[benbovy]

Thanks @dcherian, that's a good check to have I think. Most (if not all?) errors seem to be multi-index level variables that wrongly have their dimension name set as IndexVariable .name. I haven't looked into it yet but there might probably be an easy fix (hopefully!).

[dcherian]

Can we remove the name property instead or is that much much harder?

[benbovy]

This would be better indeed but this is likely more work (not sure how much, though).

IndexVariable still needs a deeper refactor (#8124), or even be eventually dropped?

[dcherian]

Where is the .name property used?

[benbovy]

After a quick check: internally only in a few places (conventions / multiindex check, dataarray creation, maybe groupby?) actually.

Externally I have no idea (IndexVariable is public API in theory).