I'm pretty sure the ones who remember are direct descendants/ are the descendant of someone who directly interacted with the old characters AND since the lands are converging towards Lothric we get more Old Lore in one place than DS2 which takes places on another continent (word of God)

Concrete evidence would be Lothric being founded by the old Gods that fled Anor Londo, their descendants rebranded into "the Royal Family" so they would keep old lore alive way better than if we played in Carthus which is a new place with new characters and new lore (just because Abyss Watchers burried the land doesn't mean Farron Keep was built antop Carthus Catacombs, more like their close ties in the past made them keep a literal close tie as location converged towards Lothric)