
Proverbs 30:4 is a riddle (Proverbs 1:6), or more precisely a double riddle: "What is his name, and what is his son's name?" The first question is easily answered, as the previous 4 lines are rhetorical questions which clearly point to Yahweh, the Lord God of Israel, particularly as he describes himself in Job 38-41. To the second question, the Christian will want to answer "Jesus!" but this answer is disqualified because it would be inaccessible to Proverbs' original audience. Lest any suggest this might be a prophecy of Christ, that answer is more strongly disqualified because it is heresy: the Son of God is God; he himself is Yahweh, the Lord God of Israel, and thus is not his own son.
I prefer to look more closely within the context of Proverbs 30 to find "his son," especially since this is the only work of Agur which we have. The only other mention of a "son" in Proverbs 30 is in the aforementioned Proverbs 30:1: "Agur, son of Jakeh." If that's so, then Agur is the son of Proverbs 30:4 and "Jakeh" is a name for the Lord. Back in the 1970s, P. Skehan suggested "Jakeh" might be an acronymn (in the original Hebrew) for "Jahweh, blessed is He." I tend to think Skehan is correct on that; even if not, the simplest answer to Proverbs 30:4 is that Agur is a son of the Lord.
As Proverbs 30:1-9 makes clear, Agur is the Lord's son because he has learned to depend utterly and absolutely upon his God. In particular, he depends on God's every Word (Proverbs 30:5-6).
That, I think, is why Proverbs 30 was placed towards the end of the book. Even a casual glance at the preceding twenty-nine chapters indicates the book's governing metaphor is a father giving Biblically-based advice to his son. Because Proverbs is Scripture, that father, ultimately, is the Lord. Agur learned wisdom by depending entirely on God's Word, and has become a faithful son of the Lord. The editors of Proverbs suggest, in turn, that if you have learned the wisdom of the Proverbs, you too are a faithful son of God.