St. Ambrose prominently mentions the significance of the Forerunner's naming in his commentary on Luke, read at Mattins today: "His name is John that is, it is not for us to choose a name now for him to whom God hath given a name already. He hath a name, which we know, but it is not one of our choosing." Augustine's teacher continues: "Thus was it that our Lord Jesus was named before He was born, with a name not given by an Angel, but by the Father. Thou seest that Angels tell that which they have been bidden to tell, not matters of their own choosing."
The Bible recounts many occasions when the Lord has given a man a new name a makes him a new person in that same moment. Abram became Abraham and the father of men as "numerous as the stars" in faith. Peter was not the first called of the Apostles—that honor went to Andrew—however he was made the "rock" upon which the Church was to be built; the "one church" and its "one chair" found its place in Peter, according to St Cyprian. Most famously in the New Testament is the case of St. Paul. Saul was a Jew keen not only on the Law, but the persecution of the Church; as Paul he would be the "doctor to the Gentiles" and the sower who planted the seeds for the conversion of the Mediterranean world. We continue this in part at Baptism and Confirmation when the neophyte receives a new name by which God knows the person and which replaces the colloquial name known in the prior life. The new name is new life and new creation.
None of this applies to John. He did not become anything. He was not refashioned into a new and better person. He was a man conceived of a woman like us, but born like Jesus and Mary, fully what God wanted him to be, fully holy, fully human. None of this would be so apparent had Zachariah not had to dispute his son's name with his wife. No one debated the name of Moses or Solomon. No one cared much about the name of John the Evangelist. They did care about the name of the Forerunner. His purpose and his purity were to him by God before he was even born. Abram, Simon, and Saul had to wait. What he was in the desert he was destined to be from eternity.
He was fully human like us, and the prefigurement to the One Who was fully human and fully divine. "God became man," wrote St. Athanasius in On the Incarnation, "so that man might become God." Despite his perfection, St. John the Baptist was still a prophet of the old covenant, which possessed the Law, but not grace (John 1:17). John's humanity was one un-encumbered by sin and spent, likely, living in the desert with the Essenes—an aesthetic sect of Judaism which valued personal austerity over outward devotion. John did not have the grace of Sacraments, into which "Christ's work has passed" according to Leo the Great. He was the most a man of the old covenant could be. Christ, imbuing the Sacraments with divinity and allowing the recipients of them to receive God in fact and symbol, is its fulfillment and, worrisome for us, is the most a man of the new covenant could be. John had his name given to him by God. All those baptized have the name Christian, "little Christ."