I fully agree, sometimes one gets to see the question about who owns the ck in a battleground, and since that doesnt seem to be shown in the /keeps - overview it really would help a lot if one knows about that, also for the purpose of giving taskitems for example. Not everybody wants to log over to a certain level-character only to check out, if they are right now able to give taskitems in there or not.
Extra information maybe some people would find interesting, especially for the unpopulated battlegrounds, if their realm doesn't own the central keep people may want to go take it for the xp/rp.
Possible to do that, it exisst for BG on Uthgard here: https://daoc.scheffel.it/realm except for Thidranki. I sent a mail to the owner of the site, the answer was: the data for Thidranki are not available, its a bug from Mythic-EA-BS... never corrected.