As Paul implies here, the Corinthians had all been baptized into Christ’s name. Through their baptism, they have been joined not to the persons who had baptized them, but to Christ. Baptism is a sign of a personal relationship with Christ, made possible through his sacrifice for sins on the cross. (This is what makes the baptism in Christ’s name different from John’s baptism; see Acts 19:1–7.) It makes sense, therefore, that from 1 Corinthians 1:18 forward, Paul will focus in on the message of the cross of Christ.
15 so that no one may say that you were baptized in my name.