Acts 13:9

Saul - Paul. The first occurrence of the name of Paul in the Acts. Hereafter he is constantly so called, except when there is a reference to the earlier period of his life. Various explanations are given of the change of name. The most satisfactory seems to be that it was customary for Hellenistic Jews to have two names, the one Hebrew and the other Grreek or Latin. Thus John was also called Marcus; Symeon, Niger; Barsabas, Justus. As Paul now comes prominently forward as the apostle to the Gentiles, Luke now retains his Gentile name, as he did his Jewish name during his ministry among the Jews. The connection of the name Paul with that of the deputy seems to me purely accidental. It was most unlike Paul to assume the name of another man, converted by his instrumentality, out of respect to him or as a memorial of his conversion. Farrar justly observes that there would have been in this "an element of vulgarity impossible to St. Paul"

Set his eyes on him. See on Luke 4:20.