You don't really "change your address" with them when you move and you are keeping service with them, you either:
Either way, Comcast will close your old account number and assign a new one. They may or may not transfer your existing email IDs (logins) from the old account to the new one. See https://www.xfinity.com/support/articles/cancel-my-xfinity-services. Good luck!
I had a seamless move from Illinois to Vermont. Done online and over the phone to confirm everything was in order prior to the physical move. Turned in my old cable TV box at the local Xfinity store and picked up my new one for my service in Vermont the day of the move. Carried it with me in the moving truck.