Tracking the names of the first-century believersThe first-century church, better termed 'Yeshua-movement,' was known as a sect within Judaism, not outside of it. All of Yeshua's follower's were known as "the sect of the Nazarenes" (Acts 24:5), just as we see "the sect of the Pharisees" (Acts 15:5), and the "sect of the Sadducees" (Acts 5:17).
It is important to note that the name Nazarenes was at first applied to all Jewish followers of Jesus. Until the name Christian became attached to the Antiochian non-Jews, this meant that the name signified the entire Church, not just a sect. So also in Acts 24:5 the reference is not to a sect of Christianity but rather to the entire primitive Church as a sect of Judaism. Ray A. Pritz, Nazarene Jewish Christianity, pg. 15
At the time of Yeshua's ministry, there were four sects within Judaism; Pharisees, Sadducees, Essenes, and Zealots. Additionally, there were labels applied to Herodians, God-fearers, proselytes, heretics, and Judaizers.
2. For there are three philosophical sects among the Jews. The followers of the first of which are the Pharisees; of the second, the Sadducees; and the third sect, which pretends to a severer discipline, are called Essenes. These last are Jews by birth, and seem to have a greater affection for one another than the other sects have. Flavius Josephus, The Wars of the Jews, Book 2, Chapter 8
Josephus records three main sects of Judaism, but the Jersualem talmud says that there were twenty-four sectcs of Judaism (y. Sanh. 29c). It is in this environment that the early converts found themselves in. In some respects, they were similar to our denominations today, except that they all studied the Hebrew Torah and were centralized because of the Jerusalem Temple. In Acts, we see some confusion between disciples (John’s, Yeshua’s, Paul’s, etc.), but they were all known as followers of the Way. In short, we see these labels applied to the believers in Acts:
Nazarene: The label applied to Jewish believers by Jerusalem.
Good-Doers: The label given to believers by Antioch.
Acts 24:5, For having found this man a plague, who stirs up dissension among all the Yehuḏim throughout the world, and a ringleader of the sect of the Natsarenes,