General TM rights say that you may not make money using someone else's mark.
That is the purpose of TM. Protecting a makers mark.
To own a domain that contains a TM is not necessarily illegal. But you may be jumping into a lawsuit and/or risking the domain.
Some of it has to do with intent and good faith use.
If you have or can obtain some right to use the name and don't fudge the boundary as confusing the mark, you might be able to use it. i.e. joe's plumbing if your name is joe and you are a plumber, you have some rights but no guarantee yours will dominate. So subject to liable depending on specifics.
A TM is very specific to goods and/or services using that mark. And in some cases, specific to certain states only, but not many of those.
You may be able to use the same mark for other goods and services as long as there is no confusion and you are not trying to siphon those looking for someone else's mark.(making money from others mark).
This is not the complete criteria, but a starter reference.
Skinny...
You can registrar anything. But you can't use anything. And nobody in their right mind is going to find value in it, only liability.