The meaning of Christian in the Bible
(From Easton's Bible Dictionary)

the name given by the Greeks or Romans, probably in reproach, to the followers of Jesus. It was first used at Antioch. The names by which the disciples were known among themselves were "brethren," "the faithful," "elect," "saints," "believers." But as distinguishing them from the multitude without, the name "Christian" came into use, and was universally accepted. This name occurs but three times in the New Testament (Acts 11:26; 26:28; I Peter 4:16).

See more on the meaning of Christian in the Bible:
Christian {International Standard Bible Encyclopedia}

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