Arelith

Replace it simply with: "This quarter/shop is owned." If they want people to know who lives there, they can rename the quarter to include their name.

What is the point of having the character's name on it? It gives away their identity and their location when the character may wish ti remain unknown. And in-universe, it seems like the sort of thing they would have control over.

Rejected.

Character name on a property allows for settlement leaders to isolate who has what property and to be able to remove it. If you remove that capability it leads to issues.

If players are wanting to hide their identity, they should really have someone else own it and just use a key. Or enter in stealth / cover.