You don't copyright a name, it would be a trademark. In the case of trademark, the name would have to be uniquely associated with a brand or business, not a common name. I couldn't just trademark Jimmy Smith as it is a very common name. I could trademark it in conjunction with a specific business such as say, Jimmy Smith's Old Winery so that no one else could then open another Jimmy Smith's Old Winery within an area in which you have registered the trademark. You can get the trademark for each state or you can go for a national trademark if it hasn't been trademarked in any state previously.
In my past business I had a name trademarked for several states in which I operated, but did not have a national trademark. Another company was trying to get a national trademark using the same name. We worked out an arrangement whereas my company would retain the trademark for specific products and they would retain it for other products in the beverage category. If we had not reached an agreement, I would not have been able to expand under that name into other states where I didn't have the registered trademark and they would not have been able to use it in the states where I owned a trademark prior to their filing for the national trademark. A simple characters name in a book, have at it. Take care. Vern