If it is an original creative work it can be copyright protected.

If it is an original unique phrase that is used used in commerce, it can be trademark protected. You can't just trademark a name or a phrase to prevent somebody else from using it or for frivolous purposes. It needs to be used in some legitimate form of commerce. Also it cannot be something that is deemed to be generic.

I am not an expert on this, but I have looked into it, consulted with an attorney, and I do hold a registered trademark. TM

Edit: also a trademark trademark has geographical limitations. Say for example you you register a trademark but you only use it in your home state. People in other States could then use it . But if you use use it nationwide, then you are protected nationwide.