Albert Barnes Commentary 1 Samuel 24:21

"Swear now therefore unto me by Jehovah, that thou wilt not cut off my seed after me, and that thou wilt not destroy my name out of my father`s house." — 1 Samuel 24:21 (ASV)

Swear now... — This is the same request that Jonathan made in 1 Samuel 20:15. The deep, genealogical feeling of the Israelites is expressed here, as it is so often elsewhere.