The Apostle Paul was not one of Jesus’ disciples.  As far as we know, he never met, or even saw Jesus.  He was a rising star among the Jewish leaders during the time shortly after Jesus’ death, Resurrection, and Ascension; and he was a persecutor of the little band of Jesus’ followers until the day of his conversion on the road to Damascus.  He had been sent to Damascus to arrest any of the Jews he found there who belonged to the little sect of Jesus followers.

Upon his arrival at Damascus, Paul, who was then samed Saul, wass struck blind and heard the voice of Jesus speaking to him. After three days of blindness, a man named Ananias was directed by Jesus to intervene:

Acts 9:17-19

So Ananias departed and entered the house. And laying his hands on him he said, “Brother Saul, the Lord Jesus who appeared to you on the road by which you came has sent me so that you may regain your sight and be filled with the Holy Spirit.” 18 And immediately something like scales fell from his eyes, and he regained his sight. Then he rose and was baptized; 19 and taking food, he was strengthened. ESV

This is the conclusion of the story of the Conversion of Paul.  Upon his recovery from his blindness and his conviction that he was called to ministry in the name of Jesus, Saul was immediately baptized and began a new life in the service of the Lord he had been persecuting,  Saul took the name of Paul at some time later in his ministry.  The changing of names upon entering a new chapter of life and ministry has become something of a phenomenon in Christianity ever since.