I'm not wanting to step on the feet of Nijay Gupta (who is of course a real scholar), but I had been planning for some time to dawdle through James Dunn's second volume, Beginning from Jerusalem, which covers the early church from after Jesus to AD70. I defer to him anyway, since he will read it 1) much more speedily and 2) he will actually finish it.
My first dawdle only made it to page 17. In these first few pages, Dunn tries to decide how to refer to the early Christians. I struggle with this question quite often too, like in this piece. He rightly rejects "Christians," since the earliest Christians didn't call themselves that. The "church" is misleading, since churches were local assemblies, not the church universal. Synagogue is fair enough, but it faces a similar debunking for Judaism that church does for Christianity.
Disciples--not widespread in the NT beyond Acts, so probably not a widespread self-description. Believers is a good candidate, one I use often. "Those who call on the name of the Lord"? Too cumbersome. "Brothers," "saints," "the elect," "the poor," nah.
How about "the way," the sect of the "Nazarenes," the "Galileans"? In the end Dunn concludes that the earliest Christians simply did not have a single term by which they referred to themselves or by which they were known to outsiders. They were a diverse group whose main point of continuity was continuity with the mission of Jesus. And they retained a distinctively Jewish character.