Read Acts 11.
The transition continued as Gentiles came to faith in Jesus and Jewish believers moved from Law and traditions to grace. During this time, the questions and misunderstandings would have been predictable. Indeed, the tension builds up to chapter 15.
When Peter explained what had happened, the questioners "glorified God" that the Gentiles were repenting of their sin and believing in Jesus as they did. The Holy Spirit made it plain that there is "no distinction" (v.12) and, even stronger, Peter added, "who am I to stand in God's way?" This seems to be clear that those who continue to treat people differently because of their race do stand in God's way.
The geographical spread of the Gospel is carefully tracked in the book of Acts. The persecution of believers in Jerusalem had caused them to flee into other parts of the Roman Empire. Peter had been in the coastal city of Joppa. He journeyed north to Cornelius' home. This area was known as Phoenicia. But they were also aware that believers had left the country and gone to the island of Cyprus and Antioch, Syria.
Next, the church in Jerusalem sent Barnabas to encourage those in Antioch. Realizing that teaching help was needed and some time had passed, Barnabas personally enlisted Saul from Tarsus in the Roman province of Cilicia. This dynamic partnership solidified the church at Antioch over time. It was here that believers were first called Christians. That was not a denomination but a label that they were committed followers of Jesus Christ. It separated them from Judaism. The term is only used here, in Acts 26:28, and in 1 Peter 4:16: "Yet if anyone suffers as a Christian, let him not be ashamed, but let him glorify God in that name."
Carrying the name of Christ as one's label in life is a sobering responsibility. Glorifying "that name" requires daily discipline of one's thoughts, speech, and actions.