Well, they can try. About five miles from here there’s a sarcophagus where the dead guy had part of his genealogy carved on the side, and there’s about an 800 year gap, but he shows one of the Companions and immediate descendants.
There’s not a single list of them and what happened to them, unless it’s been done recently online. There was an ad hoc metal plaque on the Battle Abbey, but that vanished (probably pried off by some metal scavenger) a couple hundred years ago, and probably didn’t antedate the 16th c anyway.
Add to that, the posh tended to crawl all over each other like a box of drunken hamsters, making the paper pedigree not 100% reliable. On paper, and like probably everyone on here, I’m descended from Wm the Conqueror, Alfred the Great, Charlemagne, etc, but there isn’t a big archive full of birth certificates, nor is there (usually) any DNA to be sequenced, and almost definitely none from the generations of hardworking commoners who carried the line for three, four, five hundred years from the “gateway ancestors”.
Apparently his descendants are still with us: https://www.fox10tv.com/2022/08/11/bronze-service-seals-stolen-veterans-memorial-cemetery-vandalized-over-weekend/
Dickens mentioned the Battle Abbey, and reported that it was an old, broken down, ivy-covered mess of stones..............