The words "prayer" and "request" mean basically the same thing and emphasize that Yahweh recognized that Solomon's request was sincere. See how you translated similar words in [1 Kings 8:28](../08/28.md). Alternate translation: "your request" (See: [[rc://en/ta/man/translate/figs-doublet]])
The name is a metonym for the person. Alternate translation: "to dwell there and to claim possession of it forever" (See: [[rc://en/ta/man/translate/figs-metonymy]])
The eyes and heart are synecdoche for the whole person. Alternate translation: "I will protect and care for it" (See: [[rc://en/ta/man/translate/figs-synecdoche]])