Barnabas sought Paul, “And when he had found him, he brought him to Antioch. So it was that for a whole year they assembled with the church and taught a great many people. And the disciples were first called Christians in Antioch.” (Acts 11:26)

Who Called them this? This name probably came from the Greeks / Romans who had disdain for the followers of Jesus. The name the disciples were often called was “the way” (Acts 24:14) "But this I confess to you, that according to the Way which they call a sect, so I worship the God of my fathers, believing all things which are written in the Law and in the Prophets.”

The way was used to describe their relation to Christ. The term the way was often used as describing  ones character and life. 2 Peter 2:21 For it would have been better for them not to have known the way of righteousness (we also see the way of Balaam 2 pt.2:15 and the way of Cain (Jd.1:11)

The name the Church used among themselves were “brethren,” “the faithful,” “saints,” “believers.” But the name “Christian” was accepted among the non believers according to history. This name occurs three times in the New Testament (Acts 11:26; 26:28; 1 Pet. 4:16).

By the time Paul is brought before Agrippa it is well accepted, as he says to Paul, “You almost persuade me to become a Christian.” (Acts 26:28).

Christian became the accepted name for the followers who were loyal to ‘Christ.’ Whether the term was one of derision; or identifying a group it is not possible to know for certain.  

Later on Peter uses the name Christian for the church 1 Pet 4:16 “Yet if anyone suffers as a Christian, let him not be ashamed, but let him glorify God in this matter.”

The name Christian is found in the early 2nd-century literature, and has stuck with the church throughout the centuries, it identifies those who truly follow Jesus whether they are in the local church or not.

The name Christian may also have to do with being a martyr for the faith, as Jesus said you will be my witnesses, (in Greek martyrs), one who bears witness by his death.