If your boat is titled and registered in Arizona, I don't think that the Arizona authorities much care what you put on your transom. If sailing to foreign countries, you might want to consider documenting your boat with the USCG, and dropping the state title.
U.S. boaters cruising to foreign countries usually prefer federal documentation
to attain certain protections afforded by the US flag, which include aid from the US consulate when you are in need. Foreign port officials will easily recognize federally documented vessels when clearing in. They may or may not look favorably on state documentation. It probably depends on how used to seeing state titles they are.