Yep, you need to go to get your permit “amended” for your new address, similar to getting another pistol added.
Here’s the kicker… If you have a concealed carry no-restriction permit in the county you used to live in, the judge from the new county can put a restriction on it so you lose the concealed carry. I know some people that have moved from their issuing county and haven’t gotten their driver’s license or permit changed to the new county for this reason alone.
Pretty much, most judges around here (I’m in Albany county) will look at it this way…
If you are only using your pistol for target shooting and hunting (which is pretty much all you should put on your app for why you want one, NEVER say it’s for self defense or protection, you’ll most likely get denied), the judge will put the restriction on it that you can only hunt or target shoot with it. Essentially if you don’t absolutely need it, you have no reason to have it, thus you won’t get it.