Not what, who. They would have to change their name if they moved, though.
I don't think they're the most likely team to move at all - that honor belongs to the Jaguars. New owner, shitty state to play in (very low attendance numbers for all three Florida teams, this would help all of them) and a team that's been unexciting for their entire lifetime. Next would be either the Chargers or the Raiders, as it wouldn't be a big deal for them (though I guess both would be possible, I hadn't really considered it). The Rams are also possible, but I think the Jags will be the ones to go.
Teams don't have the choice of what division they're in - they'll be forced to move. The NFL would probably decide it'd be less hassle to move them than to keep the divisions the same.