To say that Christ was called Nazarene because He was from the town of Nazareth doesn't make much sense.
Although the historian Flavius Josephus (AD 37 – c. 100) mentions 45 towns in Galilee, he never mentions Nazareth.
The earliest known reference to Nazareth outside the New Testament and as a contemporary town is by Julius Africanus, who wrote around AD 200.
That Christ was a Nazarene is actually upheld in the Roman annals; and the first-century chronicles of the Jews and the Bible's Acts of the Apostles confirm that Christ's brother James was a leader of the sect of the Nazarenes.
What I've sourced from St. Jerome's writings says, that the first believers in Christ were known as “Nazarenes” or in Hebrew “Netzarim” (Acts 24:5).
The “church father” St. Jerome (3/4 th. century AD.) described these Nazarenes as those
“…who accept Messiah in such a way that they do not cease to observe the old Law.” (Jerome; On. Is. 8:14).
In the letter to St. Augustine of Hippo, St. Jerome wrote:
Hieron., "Epist. ad August.":
"There is to-day among the Jews throughout all the synagogues of the East a heresy which is called [the heresy] of the Minaei, and is even until this day cursed by the Pharisees;
these Minaeans are commonly called Nazoraeans, and they believe in Christ, the Son of God. . . . But while they will be both Jews and Christians, they are neither Jews nor Christians."
Elsewhere I have found slightly different translation which says:
"Today there still exists among the Jews in all the synagogues of the East a heresy which is called that of the Minæans, and which is still condemned by the Pharisees;
[its followers] are ordinarily called ‘Nazarenes’;
they believe that Messiah, the son of God, was born of the Virgin Miriam, and they hold him to be the one who suffered under Pontius Pilate and ascended to heaven, and in whom we also believe.”
(Jerome; Letter 75 Jerome to Augustine)
So we know that St. Jerome (doctor of the Latin Church and author of Vulgate, the only Catholic bible for another 1000 years), knew that the first followers of Christ were in fact called Nazarenes - not Christians.
What St. Jerome said is that
"these Minaeans are commonly called Nazoraeans,..."
or we can read that
this Nazareans were in fact Minaeans.
However, what do we know today about MINAEANS ???