Should we baptized "in the name of the Father,
Son, and Holy Spirit" or "in the name of Jesus"?
The proper form of baptism is in the name of the Father, Son, and Holy Spirit as Jesus designated in Matt. 28:19, "Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit." The clear command of Jesus is to baptize this way. But, if that is so, then why do we see so many instances in the New Testament where people were baptized "in Jesus' name"?
The reason they were baptizing "in the name of Jesus" is not because it was a formula, but because the phrase, "in the name of" means "in the authority of. We can see proof of this in Acts 4:7-10,
"And when they had placed them in the center, they began to inquire, 'By what power, or in what name, have you done this?' 8 Then Peter, filled with the Holy Spirit, said to them, 'Rulers and elders of the people, 9 if we are on trial today for a benefit done to a sick man, as to how this man has been made well, 10 let it be known to all of you, and to all the people of Israel, that by the name of Jesus Christ the Nazarene, whom you crucified, whom God raised from the dead—by this name this man stands here before you in good health.'"
The Jews asked "by what power, or in what name, have you done this?" Peter answers and says that it was in the name of Jesus, that they had healed. In other words, "in the name of Jesus" means that it is by the power and authority found in Christ. We can see this usage many places in the New Testament.
As you can see, "in the name of the Lord Jesus" and "in the name of Jesus" speaks of "in the authority of Jesus." Therefore, when someone is properly baptized, they are baptized in the name of Jesus; that is, by the authority of Jesus. Therefore, when they are properly baptized in the name of Jesus, they should say, "I baptize you in the name of the Father, the Son, and the Holy Spirit," just as Jesus commanded us to do.