Again, I think the cause/effect here is backwards. If a church took a name that was outside the Bible, (i.e. Baptist, Lutheran, Methodist), that church would be guilty of violating the Sacred Doctrine Of Sola Scriptura, and therefore would not be a church.
But, basically, the CoC says nobody is a Christian who is not Baptized, by immersion, for the forgiveness of sins (among other things). So that excludes about 99% of Christianity, because, who else does that? Baptists immerse, but they don’t believe Baptism is necessary for salvation, or that sins are forgiven therein, so they’re out, along with a lot of others. Traditional churches such as Catholic, Lutheran, Orthodox all use sprinkling or pouring, so they’re out. Others just practice so-called “Holy Spirit” Baptism, so they’re out. The CoC has far greater issues than their name (I’d say “we” but technically, I’m not a member of the CoC, but the ICOC, which is an offshoot, along with several other denominations - demonstrating that the Bible-only method has its problems).