The eyes being open is a metonym for watching, and here watching represents protecting. "Please watch over this temple" or "Please protect this temple" (See: [[rc://en/ta/man/jit/figs-metaphor]])
Possible meanings are 1) Yahweh's name represents himself. Alternate translation: "where you promised to be" or 2) Yahweh's name represents his reputation. Alternate translation: "where you promised to make people know you" (See: [[rc://en/ta/man/jit/figs-metonymy]])
Solomon refers to himself as "your servant" to show that he respects Yahweh. This can be stated in first person. Alternate translation: "the prayer that I, your servant, pray toward this place" (See: [[rc://en/ta/man/jit/figs-123person]])