Sabellian view of the Godhead, represented primarily by the United Pentecostal Church, there is a believe that the description of baptisms is to be normative, and, therefore, baptisms are to be done, not in the Trinitarian formula of Matthew 28:19, but rather in Jesus's name only. In their theology, this is a salvation issue. A person cannot be saved without their baptism.
Let me grant up front that the baptisms mentioned in Acts all say something to the effect of "in the name of Jesus." What I deny is the significance that the Oneness give to that.
Look first at the Matthean formula: "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit" (Matthew 28:19). The trinitarian implications are obvious, since we have the one name, not names, for three Persons. the Oneness people point out, correctly, that we never see that formula in Acts. They then claim, with zero manuscript support, that, therefore, the trinitarian formula was added later.
However, their arguments miss several points. First, the words of Jesus in Greek, something which is not clear in the English, indicate that baptism is "into" the name of the trinity. The preposition in Acts 2:38, on the other hand, means "on account of," not "into." Thus, we have, not contradictory statements, but rather references to two distinct things. Jesus in Matthew is talking about baptism as the visible sign of the relationship of the believer to God, in His triune nature. Luke in Acts, on the other hand, is talking about the Apostles, who, by the authority of Jesus, are giving the sign of baptism to new believers.
In Acts, the emphasis is on the movement between the earthly ministry of Jesus seen in the Gospels, to the ministry of the Apostles as His representatives in Acts. the pouring out of the Spirit in chapter 2 was the visible sign of His enthronement in heaven subsequent to his ascension. Then the rest of the book is about the newfound power, authority, and prominence of the Apostles. Therefore, "in the name of Jesus" is not a formula spoken at the baptism, but rather an insistence that baptizing is the sign of the succession of the Apostles to the leadership of the Christian community. The Oneness folks never seem to notice that their formula is also not repeated anywhere else in Scripture. If it is a salvation issue, is it not reprehensible that Paul, Peter, and John never mention it in their epistles?
That's Paul's point in I Corinthians 1:14-17: "I thank God that I baptized none of you except Crispus and Gaius, so that no one may say that you were baptized in my name. (I did baptize also the household of Stephanas. Beyond that, I do not know whether I baptized anyone else.) For
Christ did not send me to baptize but to preach the gospel, and not
with words of eloquent wisdom, lest the cross of Christ be emptied of
its power." He makes a complete separation between the message of salvation, which he saw as his calling, and the rite of baptism, which was not. That is a distinction that he could not have made if he believed that baptism is a part of salvation!