"If it’s filed as a name-change, the Ministry will be informed and your records with them changed accordingly. If it’s filed as a new identity, there will be no connections between the new name and Harry Potter. With us, the Potter inheritance will remain dormant, and instead default to, as you said, the most suitable available heir. If anyone, like Albus Dumbledore, wishes the inheritance to revert back to Potter, the child would need to be produced and identity confirmed by Gringotts own staff."