en_tn/1ki/08/20.md

has carried out the word that he had said

This is an idiom. Alternate translation: "has done exactly what he said he would do" (See: rc://en/ta/man/jit/figs-idiom)

I have arisen in the place of David my father

Height is a metaphor for power. Alternate translation: "I have gained the power that David my father had" (See: rc://en/ta/man/jit/figs-metaphor)

I sit on the throne of Israel

The throne is a metonym for the activity of the one who sits on the throne. Alternate translation: "I rule over Israel" (See: rc://en/ta/man/jit/figs-metonymy)

for the name of Yahweh

The word "name" is a metonym for the person, and "for ... name" refers to worshiping the person. See how you translated this in 1 Kings 3:2. Alternate translation: "in which people will worship Yahweh" (See: rc://en/ta/man/jit/figs-metonymy)