For me, they'd have to relocate AND change their name.
I could handle a relocation (I relocated), but I wouldn't be happy about it. If they relocated and changed their name, it would be only a few seasons before any semblance of continuity was left, and they might as well be the Chargers-- which is the team I'd switch to, now being an LA resident and all.
Or I'd start watching baseball, and be a Dodgers fan, instead. Baseball is a lot less stressful, after all. I'd probably live longer.