en_tn_condensed/1ch/22/10.md

a house for my name

Here "name" refers to honor. Alternate translation: "a temple to honor me" (See: rc://en/ta/man/translate/figs-metonymy)

He will be my son, and I will be his father

God will treat Solomon as if he were God's own son. (See: rc://en/ta/man/translate/figs-metaphor)

I will establish the throne of his kingdom over Israel forever

Here "throne" refers to the authority to rule as king. Alternate translation: "I will make his descendants rule over Israel forever" (See: rc://en/ta/man/translate/figs-metonymy)