Short answer
No. Jesus never used the word Christian. It appears only three times in the whole Bible, and never in the four Gospels of the New Testament. Acts says the disciples "were called Christians first in Antioch", years after Jesus had gone. It does not say that Jesus gave the name, or that the disciples chose it. The next time the word appears, a king who had not become a Christian speaks it. The Qur'an gives another name. It records that the disciples of Jesus asked him to bear witness that they were Muslims, those who submit to God (﷾). The Qur'an says God (﷾) gave that name to all who submit to Him, and the followers of the Prophet Muhammad (ﷺ) still carry it.
Full explanation
Three verses, and none from Jesus
The word Christian occurs three times in the New Testament. It is used twice in Acts and once in First Peter. It never occurs in Matthew, Mark, Luke or John, so Jesus is never recorded using it, of himself or of anyone else. Acts puts its first use at Antioch, a city of ancient Syria. There Barnabas brought Saul (the man later called Paul, a Christian missionary of the first century), and they taught for a whole year. This was well after Jesus had gone. The verse says the disciples "were called" Christians. It does not say who gave the name, and it does not say the disciples chose it. The second use is by King Agrippa, a first-century ruler who had not become a Christian. He said to Paul: "Almost thou persuadest me to be a Christian."
“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.”
“Then Agrippa said unto Paul, Almost thou persuadest me to be a Christian.”
The word Christianity came later still
The word Christianity does not appear in the Bible at all. Its earliest known use is in a letter of Ignatius, a bishop of Antioch, written early in the second century on his way to death in Rome. He wrote that it is absurd to profess Jesus Christ and to live like a Jew, for Christianity did not believe in Judaism, but Judaism in Christianity. By then a new religion was being named over against the faith Jesus practised. Jesus had said he came not to destroy the law. Decades after him, the believers of Jerusalem were still, in the words of Acts, all zealous of the law.
Ignatius, writing on his way to martyrdom in Rome, warns the Christians of Magnesia against keeping Jewish ways. He says it is absurd to profess Jesus Christ and to Judaize, for Christianity did not believe in Judaism, but Judaism in Christianity. It is the earliest known use of the word Christianity.
“Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil. For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.”
“And when they heard it, they glorified the Lord, and said unto him, Thou seest, brother, how many thousands of Jews there are which believe; and they are all zealous of the law:”
- Jesus' ministry
Never used
The word Christian is not in Matthew, Mark, Luke or John.
- Years later, in Antioch
First called Christians
Acts says the disciples were called Christians first there; it does not say who gave the name.
- Paul's trial
On a king's lips
King Agrippa, not a Christian, uses the word.
- Early 100s
Christianity
Ignatius of Antioch gives the earliest known use of the word.
Why Christians honour the name
Christ is the Greek word for Messiah, the anointed one. Christians take the name Christian to mean one who belongs to the Messiah. They point to First Peter. That letter tells believers not to be ashamed if they suffer as a Christian. Yet the name is still never recorded on the lips of Jesus.
“Yet if any man suffer as a Christian, let him not be ashamed; but let him glorify God on this behalf.”
The name the Qur'an gives his followers
The Qur'an also calls Jesus the Messiah (al-Masih in Arabic) and honours him in this world and the next. But the name it gives to those who followed him is Muslim, one who submits to God (﷾). It records the disciples of Jesus asking him to bear witness that they were Muslims. It says Abraham was neither a Jew nor a Christian, but one who submitted his will to God (﷾).
“Behold! the angels said: "O Mary! Allah giveth thee glad tidings of a Word from Him: his name will be Christ Jesus, the son of Mary, held in honour in this world and the Hereafter and of (the company of) those nearest to Allah;”
“When Jesus found Unbelief on their part He said: "Who will be My helpers to (the work of) Allah?" Said the disciples: "We are Allah's helpers: We believe in Allah, and do thou bear witness that we are Muslims.”
“"And behold! I inspired the disciples to have faith in Me and Mine Messenger: they said, 'We have faith, and do thou bear witness that we bow to Allah as Muslims'".”
“Abraham was not a Jew nor yet a Christian; but he was true in Faith, and bowed his will to Allah's (Which is Islam), and he joined not gods with Allah.”
A name given by God (﷾)
The Qur'an says God (﷾) Himself named the believers Muslims, both before the Qur'an and in it. Ibn Kathir was a scholar who explained the Qur'an, and he died in 1373 CE. He reports that Ibn Abbas, Mujahid, Qatadah and others say "He" in that verse is God. A few read it as Abraham. Either way the name comes from revelation, not from a council or from outsiders. The Prophet (ﷺ) told believers to rally under the names Allah gave them: Muslims, believers, servants of Allah (﷾). They were not to rally under the tribal cries of the age of ignorance (the time before Islam). That hadith is graded sahih (authentic) on sunnah.com. Two Muslims once rallied their sides with "O Ansar!" and "O Emigrants!". The Ansar were the helpers of Medina, and the Emigrants were those who had left Mecca. The Prophet (ﷺ) called it a call of the age of ignorance and told them to stop.
“And strive in His cause as ye ought to strive, (with sincerity and under discipline). He has chosen you, and has imposed no difficulties on you in religion; it is the cult of your father Abraham. It is He Who has named you Muslims, both before and in this (Revelation); that the Messenger may be a witness for you, and ye be witnesses for mankind! So establish regular Prayer, give regular Charity, and hold fast to Allah! He is your Protector - the Best to protect and the Best to help!”
Reports from Ibn Abbas that "He has named you Muslims" refers to Allah, and names Mujahid, Ata, al-Dahhak, al-Suddi, Muqatil ibn Hayyan and Qatada as holding the same view. Mujahid explains that Allah named the believers Muslims before, in the earlier scriptures, and "in this", the Qur'an.
Al-Harith al-Ash'ari reports that the Prophet (ﷺ) commanded the believers to hold to the community (al-jama'a), warned that whoever leaves it by a hand-span has thrown off the bond of Islam, and said that whoever raises the call of the age of ignorance belongs to the Fire, even if he prays and fasts. He told them to call themselves by the names Allah gave them: Muslims, believers, servants of Allah.
Jabir reports that on a campaign an Emigrant struck a man of the Ansar in jest. The Ansari cried out for help to the Ansar, and the Emigrant cried out for help to the Emigrants. The Prophet (ﷺ) came out and asked why they were raising the call of the age of ignorance, and told them to stop, for it was a foul call.
Verse by verse
1 Peter 4:16 — First Epistle of Peter, chapter 4, verse 16
“Yet if any man suffer as a Christian, let him not be ashamed; but let him glorify God on this behalf.”
Cited for
A disciple of Jesus uses the name and tells believers to wear it with honour, so it is the church's own name from the start.
The response
First Peter tells believers not to be ashamed if they suffer "as a Christian". It was the name they suffered under. The letter accepts it, but it does not say that Jesus gave it. Jesus is never recorded using it. Acts says only that the disciples "were called" Christians at Antioch.
Where it lands — The name comes from the time of the first disciples, not from Jesus. The Gospels never use it.
Acts 11:26 — Acts of the Apostles, chapter 11, verse 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.”
Cited for
The Greek verb in Acts 11:26 means the disciples were divinely called Christians.
The response
The same verb is used in Romans 7:3, where a woman who marries again while her husband lives "shall be called an adulteress". There it plainly means to be known by a name. Nobody says God (﷾) gave her that name. In Acts 11:26 God (﷾) is not mentioned at all. Acts does not say who gave the name, and Jesus never used it.
Where it lands — Acts records a name the disciples were given; it does not say God (﷾) or Jesus gave it.
Perspectives
Mainstream Christian
The name means a follower of Christ, the Messiah. It arose among the first disciples' own churches at Antioch, and First Peter treats it as a name to bear with honour.
Acts places the first use of the name among the disciples at Antioch, in the first disciples' own generation.
Rebuttal
Acts does place the name at Antioch, years after Jesus had gone. It says only that the disciples "were called" Christians. It does not say who gave the name, or that Jesus did. Its next use is by King Agrippa, who had not become a Christian.
First Peter tells believers not to be ashamed if they suffer as a Christian.
Rebuttal
First Peter does use the name, as the name believers suffered under. It does not say that Jesus gave it. Jesus is never recorded using it, and Acts says only that the disciples "were called" Christians.
The Islamic perspective
Jesus never used the name Christian. In the Qur'an's account, his disciples called themselves Muslims. That is the name God gave to everyone who submits to Him, before Islam and after it.
The word Christian never appears in the four Gospels, so Jesus is never recorded using it.
Acts says the disciples were called Christians at Antioch. It does not say that Jesus or the disciples chose the name.
The second use of the word in the New Testament is by King Agrippa, who had not become a Christian.
The Qur'an says "He has named you Muslims"; Ibn Abbas and the early commentators say He is God.
The Qur'an teaches that the disciples of Jesus called themselves Muslims. It says Abraham was a Muslim, not a Jew or a Christian.
The Prophet (ﷺ) told believers to rally under the names Allah gave them: Muslims, believers, servants of Allah (﷾). They were not to rally under the tribal cries of the age of ignorance. When two Muslims rallied their sides as Ansar and Emigrants, he called it a call of the age of ignorance.