I moved and I still support my old team (Sharks). Though with my team being a basement team, I have been rooting for the closest team to me (Stars).
If the Sharks moved from San Jose... I'm not sure. The whole team is completely different than just a couple of years ago anyway. I still feel like San Jose is "home" to me. It depends on where they moved to. If they moved to Houston, I would be fully on board. They would (barely) be the closest team to me anyway, as I live about halfway between Dallas and Houston. But if they moved to like Salt Lake City or Quebec? Idk. I can't say for sure. It would certainly be devastating, and I would need to do some self-reflecting to know for sure. I might just jump over to the Stars full time.