call __finalize__ in more methods
- [ ] closes #xxxx
- [x] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [ ] whatsnew entry

The goal here is to make progress on some of the more uncontroversial/easier content of #28283. I'll split off into another PR if this gets too big
cc @TomAugspurger 

lgtm. https://github.com/pandas-dev/pandas/pull/37205 handles the dataframe.name issue.

I don't know if we want to add a test case for all of those, but one or two might not hurt? > #37205 handles the dataframe.name issue.
> 
> I don't know if we want to add a test case for all of those, but one or two might not hurt?

Great! 

I can add the tests here and then probably we would want to merge #37205 before this goes in can you merge master and ping on green as merged @TomAugspurger patch Green thanks @arw2019 