AP: The name "Paul" appears to be the nickname that he gives himself as a sign of the change that took place in his life. It pointed to how he went from being the Jew of Jews, traditionalist in every sense of the word, and former persecutor of the followers of Jesus to being the "slave" of God (corresponding to the Greek word δοῦλος). His mission entirely changed. Formerly, he fought zealously against the message of Jesus' followers. From Damascus forward he would focus all of his energies and efforts on the salvation of the gentiles.
To understand the name change we need to keep in mind the custom of changing an individual's name when he transitioned from being free to slave or, when already enslaved or indentured, there was a change in ownership. For example, there was a free Greek man named "Hippodamus" who had been taken into slavery during war. He was often called "Helleno," "Arcadio," "Lidio," or "Lycian", according to the region of origin. His name was changed by his owner so that the slave himself and others were always aware of the fact that his personal and social situation had been transformed.
When such a change was alluded to, there was a fixed formula both in Latin and Greek. For example, take Lucius qui et Porcellus ("Lucio who is also called "Pig"]); Manlius qui et Longus ("Manlio who happens to be called "Long"). Notice that the person's name is listed first. This is followed by the new name using the formula qui et which means "who is also called."
In Acts 13:9, we find the name change for the apostle to the Gentiles. The formula qui et is also present in Greek (Σαῦλος δέ, ὁ καὶ Παῦλος). The ὁ καί is equivalent to qui et. Translated, it reads, "And Saul, who is also called Paul." The use of this formula tells us that, according to Luke, Saul changed his name to Paul when he experienced this status change of free person to slave. From whom? ––From freedom to a slave of God and his Messiah, a point he make often in his letters.
This change takes place after his call by God to a new mission. Paul felt like he had been transformed in a radical way. He had gone from being a free man to a slave of the Messiah, "bought" by him to fulfill the task of proclaiming the gospel, which included the salvation of the Gentiles that was now possible. And it is also possible that this commercial designation (i.e., as a slave or property) is realized at one's baptism "in the name of the Messiah." In other words, it would be the same as becoming the property of the Messiah.
Why does he choose Παῦλος? The answer is simple. ––It means "small." It offered a perfect play on words with Σαῦλος and because he was always considered the least of the apostles and the last to be called an apostle. He writes this to the Corinthians:
"And last of all, as to one untimely born, he appeared to me also. For I am the least of the apostles, and not fit to be called an apostle, because I persecuted the church of God. But by the grace of God I am what I am, and his grace toward me did not prove vain; but I labored even more than all of them, yet not I, but the grace of God with me." (1 Cor. 15:8–10)Earlier in the same letter, Paul wrote the following: "But God has chosen the foolish things of the world to shame the wise, and God has chosen the weak things of the world to shame the things which are strong" (1 Cor. 1:27). This is no doubt an indirect reference to himself. It was because of this view of himself––purchasing his life and making him a slave––and based on what he believed God had done in his life––transforming him and giving him this new mission and life purpose––that Paul began to refer to himself as "Paul, the slave of Jesus Christ, called to be an apostle" (Rom. 1:1).
In conclusion, he went from being Saul the persecutor and freeman to Paul the slave of the Messiah who had been given a new mission. To call attention to this huge change in his life, the apostle changed his name: Saulos qui et Paulus, "Saul who is also called Paul." Paul understood his socio-religious status had changed. No longer a Jewish persecutor, now an apostolic preacher of the Messiah. And as an apostle, he became a slave of God and of Christ. Paul saw himself as a human instrument (Παῦλος) and a person who in and of himself was of little value, but God had chosen him for such an important mission.