When I checked at night the claim button darkened and told me who had claimed it. Only the vampire that claimed the coffin can see that it's theirs. If I use any other vampire the coffin looks unclaimed. Also there is no image when I hover over the coffin to show who claimed it like there are when I hover over the normal beds.
So conclusion it's hard to tell who claimed a coffin as only the vampire that claimed it can see that it's theirs, also as you noticed that mark didn't show up until it turned night. The fix needed is a way so every family member can see who the coffin belongs to, at any time of the day.
Lilith can't see that Vlad claimed the coffin, Vlad can see that he claimed the coffin and if you hover over beds Lilith can without problem see that Regyna claimed that bed. All family members should be able to see who claimed what coffin, just like you can with beds.
