But it's not going to help the player if they had already agreed in the past to add the alleged stalker to their friends list. Most stalker situations start as friendships gone bad.
Unless the player also changes physical data centers, the stalker is still going to have the name/world info since removing a person from your friends list does not remove them from yours. Very few players are open to changing worlds, let alone regions.
The key is the friends list. Something must be done to break that connection so if the player removes someone from their list, the other player is likewise removed from their list.
If friends list is tied to Character ID as the Lodestone is, even better. If there is a case of genuine stalking, the player working with the GMs and Technical Support could be granted a new character ID at the same time as the character is transferred and/or name changed. The only downside is that it would mean rebuilding the player's friends list but that would probably be a good thing at that point. The player would then get control back (at temporarily) of who would have them on their friends list and who wouldn't. They could ensure that only those they completely trust have them on the friends list so no one else could potentially be giving the new information to the stalker.
I'm not saying that players shouldn't have a privacy selection for character information on Lodestone if they want but it is pointless without changes to the in-game tools as well.