1520s as a noun, "a believer in and follower of Christ;" 1550s as an adjective, "professing the Christian religion, received into the Christian church," 16c. forms replacing Middle English Cristen (adjective and noun), from Old English cristen, from a West Germanic borrowing of Church Latin christianus, from Ecclesiastical Greek christianos, from Christos (see Christ). First used in Antioch, according to Acts xi.25-26:
And when he had found him, he brought him unto Antioch. And it came to pass, that a whole year they assembled themselves with the church, and taught much people. And the disciples were called Christians first in Antioch.
Meaning "having the manner and spiritual character proper to a follower of Christ" is from 1590s (continuing a sense in the Middle English word). Christian name, that given at christening, is from 1540s (also continuing a sense from Middle English Cristen). Christian Science as the name of a religious sect is from 1863.
c. 1200, "to baptize into the Christian church," from Old English cristnian "to baptize," literally "to make Christian," from cristen "Christian" (see Christian). Especially to baptize and name as an infant, hence "give a name to at baptism" (mid-15c.) and the general sense of "give a name to" anything, without reference to baptism (1530s). Related: Christened; christening.