yea, all the people you're playing with all exist on the same server (so you won't be able to interact with someone on say Corbantis if you're on sunrunner). As far as changing servers, i'm fairly confident this isn't an option but, hey, i'm not the authority on this one.
The best you could maybe do is try to make a characture of the same name on a different server. I'm not sure if names are verified against just the one server or all of them.