How did Christian come to be the name for believers?

The term Christian or Christians is only in the Bible 3 times: Acts 11:26, Acts 26:28, and 1 Peter 4:16. Acts 11:26 tells us a little bit of how the term Christian began to be used to describe the followers of Jesus. It says, "...The disciples were called Christians first at Antioch." (NIV) We are given nothing else to go with.

Acts 11:25-26 gives us a specific mention of when Christians were first called as such (emphasis mine).

²⁵ Then Barnabas went to Tarsus to look for Saul, ²⁶ and when he found him, he brought him to Antioch. So for a whole year Barnabas and Saul met with the church and taught great numbers of people. The disciples were called Christians first at Antioch.

_{–New International Version}

BibleHub's Acts Bible Timeline places this event at 42 AD (12 years after Jesus' ascension into heaven).

How did followers of Jesus come to be called Christians?

The term Christian is only used 3 times in the New Testament and each instance is referring to the first “Christians” of the early church.

“…So for a whole year Barnabas and Saul met with the church and taught great numbers of people. The disciples were called Christians first at Antioch” (Acts 11:26).

“Then Agrippa said to Paul, ‘Do you think that in such a short time you can persuade me to be a Christian?’” (Acts 26:28).

“However, if you suffer as a Christian, do not be ashamed, but praise God that you bear that name” (1 Peter 4:16).

Neither the Bible nor the Early Church followers of Jesus employed this term for the followers of Our Lord.

How and when was the word "Christian" first used? The term 'Christian' was used to describe a follwer of Christ in terms of the world, from the world’s point of view. The pagans at Antioch called the apostles "Christians" first (Acts 11:26; 26:28) and used it derogatorily because the apostles didn’t follow the commercial world of the pagans. "Christian" is an adjective, not a noun. The substance is not in the word "Christian", the substance is in the heart of the man it is attempting to describe, and which the pagan user cannot see.

Christ never called himself a Christian, Christ never called his followers Christians. The apostles never called each other Christians. Christ never used an adjective to describe himself. So how are we to identify ourselves then? The disciples called each other, "brethren", "disciples", "apostles", "servants", "believers", "followers, "the faithful", "the elect", "the called", and "saints." We can also identify ourselves as "bondservants" of Christ.

"Cristianos, Christian: a word formally not after the Greek but after the Roman manner, denoting attachment to or adherents to Christ. Only occurs as used by others of them, not by Christians of themselves. Tacitus (A.D. 96) says (Annals 15, 44), ‘The vulgar call them Christians. The author or origin of this denomination, Christus, had, in the reign of Tiberius been executed by the procurator, Pontius Pilate.’" Ethelbert William Bullinger, A Critical Lexicon and Concordance of the English and Greek New Testament (1908), p. 152.

"This name (Christian) occurs but three times in the New Testament, and is never used by Christians of themselves, only as spoken by or coming from those without the church. The general names by which the early Christians called themselves were ‘brethren,’ ‘disciples,’ ‘believers,’ and ‘saints.’ The presumption is that the name ‘Christian’ was originated by the heathen." Thomas W. Doane, Bible Myths (1882), page 567, note 3. - Should we call ourselves a Christian?

It could be noted that Antioch in the year 42 A.D. (the year in which this term was believed to have been coined) was the capitol of the Roman province of Syria (now within the region of Antakya, Turkey).

Apparently, Antioch, the capital of the Roman province of Syria (now within the region of Antakya, Turkey), was the location where "Christian" was first associated with early believers. "And the disciples were first called Christians in Antioch" (Acts 11:26).

Obviously, the term is identified with the idea of being a follower of Jesus Christ. In classical times the followers of a leader would identify themselves by a descriptive extension to their leader's name (ianus). Pompey's troops were called Pompeiani, and Caesar's were referred to as, Caesariani. The Christianus (of Latin origin, and hellenized), was similarly viewed as the descriptive term of the followers of Christ. - How did followers of Jesus come to be called Christians?

As a side note, there is a pious Christian tradition that considers the Apostle St. Peter to be the founder of the Church of Antioch and the first bishop of the Christian population established there; the Church of St. Peter is traditionally considered to be at the place where he first preached the Gospel in Antioch.