Height is a metaphor for power. Alternate translation: "I have gained the power that David my father had" (See: [[rc://en/ta/man/translate/figs-metaphor]])
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/translate/figs-metonymy]])
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](../03/01.md). Alternate translation: "in which people will worship Yahweh" (See: [[rc://en/ta/man/translate/figs-metonymy]])