Det ska vara lugnt, så länge den nya adressen är i samma land.

https://travel.stackexchange.com/questions/86278/my-home-address-will-ch...

"Each approved ESTA application generally is valid for two years or until the applicant’s passport expires, whichever comes first. A new travel authorization is required if: (1) the traveler is issued a new passport; (2) the traveler changes his or her name; (3) the traveler changes his or her gender; (4) the traveler’s country of citizenship changes; or (5) the circumstances underlying the traveler’s previous responses to any of the ESTA application questions requiring a “yes” or “no” response have changed. The associated fee will be charged for each new application submitted."

https://www.cbp.gov/travel/international-visitors/frequently-asked-quest...