Matthew Henry, the late Bible commentator, concurred with Clarke:

(2.) What honour was now put upon the church at Antioch: There the disciples were first called Christians; it is probable they called themselves so, incorporated themselves by that title, whether by some solemn act of the church or ministers, or whether this name insensibly obtained there by its being frequently used in their praying and preaching, we are not told; but it should seem that two such great men as Paul and Barnabas continuing there so long, being exceedingly followed, and meeting with no opposition, Christian assemblies made a greater figure there than any where, and became more considerable, which was the reason of their being called Christians first there, which, if there were to be a mother-church to rule over all other churches, would give Antioch a better title to the honour than Rome can pretend to. Hitherto those who gave up their names to Christ were called disciples, learners, scholars, trained up under him, in order to their being employed by him; but henceforward they were called Christians. [1.] Thus the reproachful names which their enemies had hitherto branded them with would, perhaps, be superseded and disused. They called them Nazarenes (Acts 24:5), the men of that way, that by-way, which had no name; and thus they prejudiced people against them. To remove the prejudice, they gave themselves a name which their enemies could not but say was proper. [2.] Thus those who before their conversion had been distinguished by the names of Jews and Gentiles might after their conversion be called by one and the same name, which would help them to forget their former dividing names, and prevent their bringing their former marks of distinction, and with them the seeds of contention, into the church. Let not one say, "I was a Jew;" nor the other, "I was a Gentile;" when both the one and the other must now say, "I am a Christian." [3.] Thus they studied to do honour to their Master, and showed that they were not ashamed to own their relation to him, but gloried in it; as the scholars of Plato called themselves Platonists, and so the scholars of other great men. They took their denomination not from the name of his person, Jesus, but of his office, Christ-anointed, so putting their creed into their names, that Jesus is the Christ; and they were willing all the world should know that this is the truth they will live and die by. Their enemies will turn this name to their reproach, and impute it to them as their crime, but they will glory in it: If this be to be vile, I will be yet more vile. [4.] Thus they now owned their dependence upon Christ, and their receivings from him; not only that they believed in him who is the anointed, but that through him they themselves had the anointing, 1 John 2:20,27. And God is said to have anointed us in Christ, 2 Corinthians 1:21. [5.] Thus they laid upon themselves, and all that should ever profess that name, a strong and lasting obligation to submit to the laws of Christ, to follow the example of Christ, and to devote themselves entirely to the honour of Christ--to be to him for a name and a praise. Are we Christians? Then we ought to think, and speak, and act, in every thing as becomes Christians, and to do nothing to the reproach of that worthy name by which we are called; that that may not be said to us which Alexander said to a soldier of his own name that was noted for a coward, Aut nomen, aut mores muta--Either change thy name or mend thy manners. And as we must look upon ourselves as Christians, and carry ourselves accordingly, so we must look upon others as Christians, and carry ourselves towards them accordingly. A Christian, though not in every thing of our mind, should be loved and respected for his sake whose name he bears, because he belongs to Christ. [6.] Thus the scripture was fulfilled, for so it was written (Isaiah 62:2) concerning the gospel-church, Thou shalt be called by a new name, which the mouth of the Lord shall name. And it is said to the corrupt and degenerate church of the Jews, The Lord God shall slay thee, and call his servants by another name, Isaiah 65:15. (Matthew Henry Complete Commentary on the Whole Bible; source; underline emphasis ours)

The late exegete John Gill provides evidence from a patristic father that the name Christians was employed by a Christian bishop of Syria:

and the disciples were called Christians first in Antioch;
before they were called among themselves, the disciples, brethren, believers, the church… and by others the Nazarenes, and Galilaeans: whether this name of Christians, which comes from Christ, and signifies anointed ones, was given by their enemies, or their friends, by others, or themselves, is not certain, though it is most likely the latter; and it may be they hit upon this general appellation, upon the union of the Jews and Gentiles in one Gospel church state, and so happily buried the distinction of Jews and Gentiles, or those of the circumcision that believed, and those of the uncircumcision. Luke is particular in relating the affairs of this church, he being himself a native of this place. John of Antioch ^F15 gives an account of this matter in these words;

“at the beginning of the reign of Claudius Caesar, ten years after Jesus Christ, our Lord and God, was ascended up into heaven, Evodus, the first after the Apostle Peter, being chosen bishop of Antioch, the great city of Syria, became a patriarch, and under him they were called Christians: for this same bishop, Evodus, conferring with them, put this name upon them, whereas before the Christians were called Nazarenes and Galilaeans.”

F15 Apud Gregory's Notes… p. 155. (The New John Gill Exposition of the Entire Bible; source; underline emphasis ours)

More on the point of the name being divinely appointed a little later.

Moreover, the Apostles like Paul were eager to persuade individuals to become Christian:

"Then Agrippa said to Paul, ‘Do you think that in such a short time you can persuade me to be a Christian?’ Paul replied, ‘Short time or long—I pray God that not only you but all who are listening to me today may become what I am, except for these chains.’" Acts 26:28-29

Peter, one of Christ’s closest companions, exhorted believers to rejoice at the fact that they were suffering for being Christians:

"If you are insulted because of the name of Christ, you are blessed, for the Spirit of glory and of God rests on you. If you suffer, it should not be as a murderer or thief or any other kind of criminal, or even as a meddler. However, if you suffer as a Christian, do not be ashamed, but praise God that you bear that name." 1 Peter 4:14-16

This leads me to another point. Christ specifically told his disciples that they would be given authority to speak on matters which would be binding upon all true believers:

"‘But what about you?’ he asked. ‘Who do you say I am?’ Simon Peter answered, ‘You are the Christ, the Son of the living God.’ Jesus replied, ‘Blessed are you, Simon son of Jonah, for this was not revealed to you by man, but by my Father in heaven. And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it. I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.’" Matthew 16:15-19

"I tell you the truth, whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven." Matthew 18:18

The Lord also stated that the Holy Spirit would reveal new things to them which they would then pass on to the Churches:

"I have much more to say to you, more than you can now bear. But when he, the Spirit of truth, comes, he will guide you into all truth. He will not speak on his own; he will speak only what he hears, and he will tell you what is yet to come." John 16:12-13

"Again Jesus said, ‘Peace be with you! As the Father has sent me, I am sending you.’ And with that he breathed on them and said, ‘Receive the Holy Spirit. If you forgive anyone his sins, they are forgiven; if you do not forgive them, they are not forgiven.’" John 20:21-23

The Apostles themselves claimed that they were speaking by the authority of Christ, passing on the instructions which they had received from the Holy Spirit:

"This is what we speak, not in words taught us by human wisdom but in words taught by the Spirit, expressing spiritual truths in spiritual words." 1 Corinthians 2:13

"since you are demanding proof that Christ is speaking through me. He is not weak in dealing with you, but is powerful among you… This is why I write these things when I am absent, that when I come I may not have to be harsh in my use of authority—the authority the Lord gave me for building you up, not for tearing you down." 2 Corinthians 13:3, 10

"Surely you have heard about the administration of God's grace that was given to me for you, that is, the mystery made known to me by revelation, as I have already written briefly. In reading this, then, you will be able to understand my insight into the mystery of Christ, which was not made known to men in other generations as it has now been revealed by the Spirit to God's holy apostles and prophets. This mystery is that through the gospel the Gentiles are heirs together with Israel, members together of one body, and sharers together in the promise in Christ Jesus. I became a servant of this gospel by the gift of God's grace given me through the working of his power." Ephesians 3:2-7

"For you know what instructions we gave you by the authority of the Lord Jesus… Therefore, he who rejects this instruction does not reject man but God, who gives you his Holy Spirit." 1 Thessalonians 4:2, 8

"Dear friends, this is now my second letter to you. I have written both of them as reminders to stimulate you to wholesome thinking. I want you to recall the words spoken in the past by the holy prophets and the command given by our Lord and Savior through your apostles." 2 Peter 3:1-2

What the foregoing texts imply is that even if Christ had never hinted that there would be a time in which his followers would bear his name, Peter’s statement to believers that they should rejoice for bearing the title Christian would be sufficient in and of itself to demonstrate that this is in fact a divinely revealed name. Seeing that the Lord Jesus personally gave the disciples like Peter the authority to speak on issues which he himself may have not addressed while on earth indicates that Peter’s use of the term Christians actually came from God. It was God who bestowed it upon the followers of Christ through his inspired spokespersons and agents. It didn’t originate from Peter, or the other Apostles, but was revealed to and through them to the Churches.

To put it simply, the word Christian is not a man-made title but an inspired name which God bestowed upon all true believers. It is divine, not human, in origin.

Unless stated otherwise all scriptural quotations taken from the New International Version (NIV) of the Holy Bible.

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