Acts 19:1-5 provides precedent for a person being “re-baptized” when his previous baptism was not according to scriptural instructions. In the case of the persons in the text they had been immersed according to the preaching of John the Baptist, which had only anticipated the redemptive work of Christ. John never baptized in the name of Jesus. Baptism in Jesus’ name began on Pentecost (Acts 2:38; cf. Luke 24:46f). They needed to know and believe that John’s preparatory work had been finished and that the “one baptism” of the Christian dispensation must be in Christ’s name.
The issue, however, is not whether one’s baptism is said to be “in the name of Christ.” Much error and evil occurs with mere claims of being in his name (Matt. 24:5; Acts 19:13ff). Various baptisms performed in various groups may be said to be in Christ’s name, but are not in fact if they are not in harmony with Christ’s instructions. Only when a penitent believer is being baptized that his sins might be washed away is he “calling on the name of the Lord” (Acts 22:16). – DRP