Gerald - this is a really tricky subject and nobody should offer you legal advice on a forum, nor should you rely on advice from a forum, even from lawyers or legal professionals.
However, a couple of thoughts: You shouldn't use your name on a resonator guitar if your name is Dobro, for example. That one is taken. Do a search on the web, and the
http://www.uspto.gov website and see if your name pops up in connection with guitars. If you get nothing, you might be good to go. If you are really going into business, you might ask a trademark lawyer to confirm that there is no problem.
The original resonator guitar patents date back to the 1920's I think, and are long expired. Have there been any improvements or changes since then? If not, it seems likely, like other traditional instruments, that the basic design is in the public domain. See above!