Legal Question in Business Law in California

Hard to say, because the right to use a name that has become a trademark in one area may or may not preclude its use for a completely different area. I think if you were going to use "Howdy Doody" for a puppet shop, or "Gunsmoke" for a private detective service, you might be in trouble. Using the same names for foot-long hot dogs or a cologne, respectively, might be much safer.

Trademark infringement is based more on the likelihood of confusion than on similarity of name. If you are manufacturing shock-absorbing devices in Dublin, you could probably call your business "Irish Spring," but that would not work if you were making bath soap, no matter where in the World.

Most old TV shows, especially the successful ones that people liked and remember, are subject to on-going copyright and trademark rights that studio and network lawyers police, even today, but rarely will they get excited about a use of a fairly generic name (like Gunsmoke) for something that has nothing to do with entertainment, broadcasting, law enforcement, etc.