I'll say that UPS will only send you automatic updates for packages that match your full address, including your name. I'm signed up for the service, and I receive uncannily perfect notifications every time a UPS label is generated with my street address and name, however I've received exactly zero notifications about my girlfriend's packages to the same address. In fact, she's independently signed up for UPS MyChoice under her name and now gets those notifications herself. It's a great service.

So, when you move, you don't really have to deactivate it so long as you don't send any more packages to that address with your name.