A PR for a package init that I was looking forward to was closed due to inactivity on the part of the author.
Would it be rude if I open a PR with the same name, with the requested changes applied? If I did that, who’s name would I put in the maintainers list?
This would be completely fine. And it wouldn’t be re-opening a pr, it would be authoring your own based off the work of another.
As for who to put in the maintainers list, I’d suggest yourself if you can.
Maintainer is the person who volunteers to continually maintain the package, i.e. apply updates and make sure it continues to work. So if the other person has abandoned the PR, they probably wouldn’t want to maintain it. So it would be great if you could do that 
If you want to give credit to the original author, you can add them as co-author to the commit: Creating a commit with multiple authors - GitHub Docs
Maintainer is the person who volunteers to continually maintain the package, i.e. apply updates and make sure it continues to work. So if the other person has abandoned the PR, they probably wouldn’t want to maintain it. So it would be great if you could do that
Failing that, a maintainer that can help investigate any issues that arise is also useful, though…