“In Antioch the disciples were first called Christians [Χριστιανούς].” (Acts 11:26)
F. F. Bruce writes, “It is natural that the designation ‘Christian’ should first have been given to the followers of Jesus in Antioch, and by Gentiles.” He explains:
1. This followed a pattern of attaching a Latin suffix to a name. “As the Herodians in the Gospels were adherents of Herod, so the Christians (christianoi) were adherents of Christ (such forms consisting of the stem of a personal name followed by an originally Latin suffix, -ianus).”
2. Non-Christian Jews would have avoided calling Jesus “Christ.” “Greek-speaking Jews at that date would not have referred to Jesus as Christ, for that was still a title (christos, the “anointed” one, corresponding to the Semitic messiah); to refer to him thus would have been to acknowledge him as Messiah.”
3. Gentiles, however, could have construed “Christ” simply as an alternative name. “But in Gentile ears Christ was simply an alternative name for Jesus; it had no such associations for them as it had for Jews.”
4. “Christos” sounded like a common slave-name. “Christos sounded exactly like a fairly common slave-name, Chrēstos (Latin Chrestus), and among Greeks and Romans there was considerable confusion between, the two spellings, as also between christianoi and chrēstianoi.”
5. The slave name sounded so similar, that some scribes copying Acts made the mistake of using it. “Even in Acts 11:26, where it is mentioned that “in Antioch the disciples were for the first time called Christians”, a few Greek witnesses to the text (including the first hand in Codex Sinaiticus) exhibit the spelling chrēstianous (accusative plural) instead of christianous. The latter is certainly what Luke wrote, but the former may well represent what some of the Antiochenes thought they were saying.”
Bruce, F. F. (1977). Paul: Apostle of the Free Spirit (p. 132). Milton Keynes, UK: Paternoster.
The Jesus-movement was otherwise (more internally?) simply called “the Way” (Acts 9:2, 19:9, 19:23, 24:14, 24:22).