Biblical Hebrew Question

In I Kings, Chapter 3:10, the following sentence says:

וַיִּיטַ֥ב הַדָּבָ֖ר בְּעֵינֵ֣י אֲדֹנָ֑י כִּ֚י שָׁאַ֣ל שְׁלֹמֹ֔ה אֶת־הַדָּבָ֖ר הַזֶּֽה׃

My Chevruta and I wondered why G-d’s name is Ad-nai and not YH-VH, as in most, if not all cases of B’einei Hashem.

When I first translated it, I thought Shlomo was speaking “to my Lord,” and then spoke of himself in the 3rd person in the 2nd part of the sentence, as if to say, “May the thing be good in the eyes, of my Lord, because Shlomo [me] asked for this thing.” Similar to a child asking a parent, “Will you see my request as good, because Joey [your son] asked for this thing.”