ADS-B is not registered to a name. ADS-B devices store the ICAO code and flight ID which are then sent in each packet. In the US your ICAO code is your encoded N-number and the flight ID for GA is generally your N-number (unless you temporarily change it for pilots n' paws/angle flight/etc). So unless you are changing the N-number of the aircraft, really the only thing you need to do is to properly register the aircraft in your name with the FAA, which hopefully you've already done, but that can take a while to update in the FAA database and then flow on out to third parties.