Should a Christian be baptized in the name of Jesus?

What is the correct baptismal formula to use? Is it that given in Matthew 28:19? In Acts 2:38 Peter says, “In the name of Jesus Christ.” In Acts 10:48 we read, “In the Name of the Lord.” In Acts 16:5 “They were baptized in the Name of the Lord Jesus.”

Does Matthew 28:19 refer to the millennium?

The commission of Matthew 28:19 was given by the Lord to His disciples before leaving them, as their immediate “marching orders,” and there is no hint that it was intended for the millennium, some far- off future dispensation, or that it was superseded by some other commission. Indeed, who had the right to supersede it? It is shallow reasoning to infer that because the formula of Matthew 28 is not specifically mentioned in the Acts, it was not used.
Then the formula of blessing in Numbers 6:23-27 was never used in the history of Israel, since it is not once mentioned! On the contrary, it was doubtless often used, and so with the baptismal formula of Matthew 28. There are two prepositions used in connection with baptism in the Acts—”en” and “eis.” The first means “in”, and with “the Name” it simply explains the authority for baptism. Peter commands them “in the Name of the Lord” to be baptized (Acts 10:48)—order of the Greek. The “eis” occurs twice: i.e., in Acts 8:16, with reference to the Samaritans, and in Acts 14:5 of the John Baptist disciples at Ephesus, in both of which cases special importance attached to the confession of the right name—”into the Name of the Lord Jesus.” But this was in no sense a formula, and we need have no doubt but that the formula of Matthew 28 “into the Name of the Father, and of the Son, and of the Holy Holy Ghost,” was used in every case. What more appropriate for a Christian dispensation, or less so for a future Jewish economy? The “epi” of Acts 2:38 has to give way to “en,” it is generally agreed. Peter here too refers back to the authority of the Lord for baptizing. And if we are doing something on another person’s authority, should we not carry out that person’s direction to the letter?

It should be noticed that in any case, a person is not saved by being batpized correctly or incorrectly.  Baptism is for a believer who has already received Christ as his savior.  See the other questions below regarding salvation and baptism.