As you may remember, up until chapter 13 Paul is known in Acts by his other name, Saul. Acts 13 records the start of Paul’s first missionary journey. Barnabas and Saul have traveled to the island of Cyprus, where they are attempting to preach the gospel to the Roman proconsul Sergius Paulus. However, they were being hindered by a Jewish sorcerer and false prophet named Bar-jesus, “who,” we are told, “was an attendant of the proconsul” (v. 7). Next we read in vv. 9–10, “Then Saul, who was also called Paul, filled with the Holy Spirit, looked straight at Elymas and said, ‘You are a child of the devil and an enemy of everything that is right! You are full of all kinds of deceit and trickery….'” Immediately, the false prophet was struck with blindness (v. 11), and “when the proconsul saw what had happened, he believed, for he was amazed at the teaching about the Lord” (v. 12).
I have heard it said, and sometimes read (e.g., Ironside), that Luke’s comment in Acts 13:9 shows that Saul sort of officially changed his name at this time. It is suggested that he decided to give up his Hebrew name Saul in exchange for the name of the illustrious convert of the first missionary journey, Sergius Paulus. But this is clearly not the case.
Paul always had the Latin name Paullus (Greek, παῦλος) because he was born a Roman citizen (Acts 22:28). Every Roman citizen had three names or tria nomina, consisting of a praenómen (forename), nómen (family name) and cognómen (personal name). Most scholars believe that Paul is the apostle’s cognomen. His praenomen and nomen are unknown. Paul also had another name, a signum or supernomen—Saul, his Hebrew name. What Luke is telling us is that Paul, “the apostle to the Gentiles” (Rom 11:13), having begun his missionary work to the Gentile world, will now appropriately use his Roman (Gentile) name.
Paul did not change his name on the island of Cyprus. Luke is simply observing that Paul chose to use his Roman name when in a Gentile context. It is strictly coincidental that Paul and Sergius Paulus have the same cognomen.