"Christian" is the name given to the disciples of Christ in Antioch of Syria following the first missionary journey of Paul and Barnabas (Acts 11:26).
The verb chrematizo ("called") in this passage suggests a divinely given name. Some think that "called" may also be a technical term that hints that it was a disciple's business to serve Christ (W. E. Vine).
Herod Agrippa II, a ruler before whom Paul appeared, declared that the apostle, with forceful persuasion, was making a case for becoming a Christian (Acts 26:28). And Peter proudly contended that those who suffer for the name "Christian" should glorify God thereby (1 Pet. 4:16).
There is no reason to believe that the early Christians adopted the name for themselves or that their enemies thrust the appellation upon them. It is a tragedy that this sacred title has been replaced today by so many sectarian designations (e.g., Catholic, Lutheran, Baptist, etc.).