From First Corinthians by George T. Montague, SM, commenting on I Corinthians 1:10-13, 17
This party spirit involves an absurdity, and Paul uses ironic rhetorical questions to expose it. Is Christ divided? Is Christ cut into pieces, so that each of the four persons would have a part? Or perhaps better, is Christ divided against himself?
Was Paul crucified for you? Here is one of the earliest written affirmations, though indirect, of the saving power of Christ’s death for those who accept it. In Rom 3:22–25, Paul will speak of the shedding of Christ’s blood as an atonement for sin, as Matthew will later report Jesus’ having said at the Last Supper: “This is [the cup of] my blood of the covenant, which will be on behalf of many for the forgiveness of sins” (Matt 26:28). Paul had surely preached this to the Corinthians, but their championing of different leaders, including Paul, seems to make saviors of those who are only instruments of Christ.
Were you baptized in the name of Paul? further skewers the absurdity. Christians were not baptized in the name of the preacher or the baptizer. The Greek says literally baptized “unto the name.” Papyrus documents from this period use this expression to mark the transfer of purchased goods from one person to another. Ascribed to the new name, the goods become the property of the new owner. For Paul, that is what baptism does: it signifies that the person is now the property of Jesus Christ. In this case the transfer of ownership is a consecration. In the Old Testament, invoking the divine name on the people means that God has set them apart as his own, thus making them holy (Deut 28:9–10; Isa 63:19; Jer 7:10; 14:9). Thus baptism “into the name” of Jesus (also used in Acts 8:16; 19:5) is a consecration of the person to God in Jesus Christ.