IN THOSE DAYS, the disciples having been scattered because of the persecution that took place over Stephen, traveled as far as Phoenicia, Cyprus, and Antioch, and they proclaimed the word to no one except the Jews. But among them were some men of Cyprus and Cyrene who, on coming to Antioch, spoke to the Hellenists also, preaching the Lord Jesus. And the hand of the Lord was with them, and a great number became believers and turned to the Lord. News of this came to the ears of the Church in Jerusalem, and they sent Barnabas to Antioch. When he came and saw the grace of God, he rejoiced, and he exhorted them all to remain faithful to the Lord with a sincere heart, for Barnabas was a good man, full of the Holy Spirit and of faith. And many people were brought to the Lord. Then Barnabas went to Tarsus to look for Saul, and when he had found him, he brought Saul to Antioch. So it was that for an entire year they assembled with the Church and taught many people. And it was in Antioch that the disciples were first called “Christians.” Then the disciples determined that according to their ability, each would send relief to the brethren living in Judea. This they did, sending it to the presbyters by Barnabas and Saul.
Saint John Chrysostom explains why the persecution that took place of Saint Stephen's death was the best thing for the young Church,
The persecution turned out to be no slight benefit, as "to those who love God all things work together for good" (Romans 8:28). If they had made it their express study how best to establish the Church, they would have done nothing else but this: they dispersed the teachers. When Stephen was slain, when Paul was twice in danger, when the apostles were scourged, then the Gentiles received the word, and also the Samaritans. Paul declared, "It was necessary that the Word of God should be spoken to you first, but since you reject it and judge yourselves unworthy of everlasting life, behold, we turn to the Gentiles" (Acts 13:46). Truly, this is the reason why it was there they were appointed to be called Christians, because Paul spent so long a time in Antioch.