MMSI belongs to the Boat if a Fixed set. A handheld DSC set will have a 2359 MMSI which is registerd to the user. Therefore if you change boats, or even take the handheld aboard another craft, there is no need to change registration.
High level theory being that for fixed sets they know what has just pressed the big red "help" button so can send appropriate SAR (e.g. for a ferry vs a 20' yacht).