Well, obvious Rimuru means it's fine to take a vacation to visit home. Not that he's kicking her out permanently.
But yeah... I wouldn't want to go to that Rabbitman village either. They took the "man" part of that village name a little too seriously. And no, random scrub, you wouldn't be "named" just because you wanted to. Obviously you need to have merits too, rather than just "happen to be walking by when Rimuru's giving out free names".