If memory serves, you can trademark your band's logo, not the actual name. No one will ever own words. (unless you're that "let's get ready to rumble" dickhead) Make sure it's worth trademarking. If you have a band name that sounds like it could be an organization or some type of entertainment company, it might be worth it to trademark. But if your name is like, "Hellspawn Demons of the Nordic Winds" I doubt you'd have much to worry about.
There are measures outside of copyright law that you can take to protect your stuff. As long as you have some kind of dated documentation that predates what someone else has, you're pretty much in the clear. You could do the poorman's copyright and just mail yourself your logo. It's dated with government seal etc. Not sure how well that would stand in court, but it's something.