Schools will require your ID and proof as address within the school district. A telephone call to the admin office of the local school district and you will be able to know exactly what they need. Banks etc will require your a iD and proof is residency and address.
Your USC fiance will surely be able to provide info on these US processes
Unlike some other countries, there is no federal state or local “ registration” of where you live or move to. The closest thing to that would be your drivers licence, which is issued by your state and requires you to update address details when you move within the state , and obtain a new state licence if you move to another state.