I'm no expert but I'm pretty sure you can't copyright just a name. Copyright protects the right to copy something, including a character and derivatives of it but I don't think it really protects a name so much.
Trademark protects a title that's in use (you can't just trademark something and own it forever though) which can be a character's name. So for example even though Tarzan is technically in the public domain the name Tarzan is trademarked, so if you slap that on your book prepare yourself to get sued by ERB inc. And in order to trademark something you'd have to have an actual product you're selling not just a name.
You would probably need to create your character, turn it into a product of some kind (comic, book, t shirt etc.) and THEN trademark it which is a long and tough process because if your name is too generic or someone else has a similar version in the same field your trademark will probably be slapped down by the trademark office.
You shouldn't worry too much about owning the name though, I'd say just make it if you want to and worry about that stuff later.