Both statements mean basically same thing. The word "house" is a metonym that represents the descendants of Israel. But, both "people" and "house" probably are a synecdoche representing the soldiers of Israel. AT: "for the Israelite soldiers" (See: [[rc://en/ta/man/translate/figs-parallelism]] and [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-synecdoche]])
This is the name of God that he revealed to his people in the Old Testament. See the translationWord page about Yahweh concerning how to translate this.
# they had fallen by the sword
Here "fallen" is a polite way of referring to being killed. Also, "sword" represents a battle. This here means "had been killed." AT: "they had died in battle" or "enemies had killed them in battle" (See: [[rc://en/ta/man/translate/figs-euphemism]] and [[rc://en/ta/man/translate/figs-metonymy]])
The man had already stated that he is an Amalekite in [2 Samuel 1:8](./08.md). David apparently asks the man to confirm this because of the serious judgment that David was going to pronounce on the man.