Solomon speaks about events that he thinks could happen in the future. The situations he describes are conditions for what he requests in the following sentence. The words "suppose that" can be translated with the word "if," and this sentence can be connected to his request in verse 35.
Solomon speaks of commanding the people to build the temple and telling them how to do it as if he himself had built it. Alternate translation: "this house that your people have built under my leadership" or "this house that I and your people have built" (See: [[rc://en/ta/man/translate/figs-synecdoche]])
Possible meanings are 1) Yahweh's name represents himself. Alternate translation: "for you" or 2) Yahweh's name represents his reputation. Alternate translation: "for your reputation" (See: [[rc://en/ta/man/translate/figs-metonymy]])