At what point did Jesus become God's son? I believe he has always eternally existed with God, but when did he inherit the title "son"? Since scriptures say that God sent his son into the world, I assume that he was referred to as the son in heaven. But was he always God's son, or did this title come to pass at some point later?

Most theologians would say Jesus' sonship preceded his birth. The Trinity has always existed. Jesus' sonship is not just a relational reality, but an analogy. In human relationships, parenthood always precedes the existence of the child. With God the Son and God the Father, this is not the case.

For example, a book may lie on the table, and normally this would suggest the table was in position before the book was laid upon it. But not necessarily. There are other ways to envision how the table came to be under the book. With God, time is not a consideration. One thing being anterior to another is not necessarily significant.

When the accession Psalm (Psalm 2) is quoted, the king "becomes" God's son on acceding to the throne. But that was normal ancient Near Eastern parlance. It is not a perfect analogy, either. Otherwise he would not have become the son of God until his ascension! Some theologians even claim that he was adopted as God's son at his baptism, on the descent of the Spirit as Jesus emerged from the water. Yet Philippians 2 indicates the kenosis, or "emptying" of himself that Jesus voluntarily underwent, was part of his incarnation. He was God incarnate, but did not cling to his divine prerogatives as such. Jesus' kenosis implied his divinity was not conferred during his earthly life (e.g., at his baptism), but preexisted it.

In short, Jesus has always been the Son of God.