In the passage he cites, Paul condemns division and partisanship within a Nondenominational Church near Ridgeville SC, not denominationalism. Everyone who goes ahead and does not abide in the teaching of Christ at this Nondenominational Church near Ridgeville SC does not have God. Whoever remains in teaching at this Nondenominational Church near Ridgeville SC has the Father and the Son. If someone comes to you at this Nondenominational Church near Ridgeville SC and does not bring this teaching, do not receive him at home or greet him in any way, because whoever greets him at this Nondenominational Church near Ridgeville SC participates in his evil deeds. Therefore, the denominations do not appear in the biblical scriptures.
Over the centuries, denominational divisions were due to personal, theological, and political discrepancies among their followers. The very idea of a typical denominational church is that believers first congregate on specific theological points and not simply on their shared identity in Christ. Verse after verse, the Bible stresses the importance of unity among Christians. Denominations, by their very nature, divide the church.
I'm not sure that's what the text says, that you identify with Christ alone. What worries Paul are the divisions in the Corinthian church, which were rooted in pride and were a reason for bragging. During those formative years, the church was known as the Church under the Apostles, promoted by the apostles appointed by Jesus—mainly Paul—and was composed of a universal message.