can a restaurant name be used more than once if that name is used in another state?What is the name of your state (only U.S. law)? Indiana
Maybe.
There is a case where "The Blue Note" in New York sued "The Blue Note" in Missouri. I think that had ore to due with their website.
There was a local case where "Sport Clips" of Texas sued "Sports Clip" of Massachusetts.
In the Blue Note case, the finding was for the Blue Note of Missouri, but that went to the US Court of Appeals, which is never an inexpensive proposition.
In the Sports Clip case, the Massachusetts company changed their name because it was easier/cheaper than fighting a legal battle.
If you're really determined to use that name, the best thing is to get permission from the other one. The next best thing is to hire a good lawyer. Actually, you should hire a good lawyer to get the permission.