Hello! This is also something that has been weighing on my mind a little.
For a town, then a lair (containing one human-form werebeast), then a hamlet, I first laid a claim to the site and then slew the lord/resident (and all witnesses). I also noted that though the inhabitants knew that I was the new lord, they didn't seem to know /how/ unless I told them, which quickly earned me their ire if so.
The part that bothered me is that though it went well for the first site, naming my new entity and getting the town, I had to name my entity again both times for the next two sites (by the way, the lair gave no announcement upon slaying the werebeast)--and then, trying to demand tribute from the lord of a fourth site, I found three options to demand tribute and three options to offer tribute.
Checking in Legends Viewer 1.13, I see three separate listings for my chosen entity name. (Edit: Removed a reference to the sites disappearing from what turned out to be the Civs view. They still appear as normal in the Sites view.)
I would very much like to gather prestige by taking over enough towns+hamlets that other sites start obeying my demands, but suspect that this will be difficult if every taken site views itself as being held by a different entity (which aren't associated with each other).
If all the entities I'm the lord of is taken into account when deciding whether to obey or not there shouldn't be a problem, granted. *wonders whether to name each entity differently, or whether there's some way for the same entity to hold multiple sites*
Edit: Also, the town went from 1315 -> 316 humans and the hamlet went from 292 -> 14 humans. *blinks* Any idea why? Were they so discontented that they all moved somewhere else, or did they vanish somehow..? I can't see any records of historical figures leaving.