That and the "skulls" difficulty of the poi remains as well. It would be nice if that also didn't exist and it showed an icon or something that indicated a player owned it. Even neater if you could choose your icon from a list (like a faction, flag, skull, rainbow, trader, whatever... if not "random" icons then just allow all the in game icons to be selected from... maybe color them).
i could see however this being an issue if three land claim was straddling 2 pois...or just a corner of one. The only possible solution i can come up with is a specific place" a land claim would have to be put down on (like a literal highlighted block indicator) that would then officially claim the poi, allow renaming, etc. that would only/mostly cover that poi with the land claim area (it would have to be in the center of any poi probably). Likely a better "solution" would be a single column of blocks you could put it jn (in the center of a poi) so you could put the claim block underground or on top of a building and not just "a single location".
It would be also be really neat especially in a modded game where you could literally take over a trader compound (or an empty one) and set up your own custom named and official looking prebuilt trader post