en_tn_condensed/1sa/24/21.md

you will not cut off my descendants after me

"you will not kill my sons and their families." It was common for a new king who was not from the previous family line to kill off all the children to prevent any of them from challenging him for the throne.

you will not destroy my name out of my father's house

"you will not destroy my family and descendants" or "you will allow my family to live"