This is really a trick question. Why? Because Paul's name NEVER changed! Paulos (Paul) is his Greek name but his real name (by birth), was Shaul (pronounced, Shaw'ool). Paul was a Hebrew rabbi who studied under Gamaliel (one of the most highly respected Pharisees in Israel), and according to Paul, was more zealous than any of his peers. Just to give you an idea of how studied this man was, one of the requirements to study under Gamaliel was to have the entire Tenach (Old Testament) memorized! Paul was not just a learned man. He was the best of the best! Which explains why some of his writings are so hard to understand. Because he was a learned scholar trying to give instructions to unlearned (in the scriptures) Gentiles who didn't have a clue! But, back to our topic; Paul would have most likely used his Greek name when doing commerce and with the Gentiles, but would have always used his native name "rabbi Shaul", when addressing the Jews and probably his converts.
Even though this is just a small truth, it just goes to show you how gullible we are to believe everything we are taught. It also shows how, once again, not knowing the culture and times in which something is written, can leave the reader to develope his own ideas and traditions. Even though this might appear to be a small issue, it can lead to very wrong conclusions. For instance, if you believe that Paul's name was changed after his conversion, then you, by default, might easily come to the conclusion that God changed everything about Paul and what he believed. Although God did very much change the character and thoughts of Paul, he nevertheless was still a Jewish rabbi that was very well respected. But now, he had a new mission.