Albert Barnes Commentary Acts 19:5

"And when they heard this, they were baptized into the name of the Lord Jesus." — Acts 19:5 (ASV)

When they heard this. When they heard what Paul had said regarding the nature of John's baptism.

They were baptized. As there is no other instance in the New Testament of any persons having been rebaptized, it has been made a question by some critics whether it was done here. They have supposed that all this is Luke's narrative regarding what took place under the ministry of John; namely, that John told them to believe in Christ Jesus, and then baptized them in his name. But this is a most forced construction; and it is evident that these persons were rebaptized by Paul's direction. For:

1. This is the obvious interpretation of the passage—that which would strike all persons as correct, unless there were some previous theory to support.
2. It was not a matter of fact that John baptized in the name of Christ Jesus. His was the baptism of repentance; and there is not the slightest evidence that he ever used the name of Jesus in the form of baptism.
3. If this is the sense of the passage, that John baptized them in the name of Jesus, then this verse is a mere repetition of Acts 19:4—a tautology of which the sacred writers would not be guilty.
4. It is evident that the persons on whom Paul laid his hands (Acts 19:6) and those who were baptized were the same. But these were the persons who heard what was said (Acts 19:5). The narrative is continuous, all parts of it cohering together as relating to a transaction that occurred at the same time.

If the obvious interpretation of the passage is the true one, it follows that the baptism of John was not strictly Christian baptism. It was the baptism of repentance, a baptism designed to prepare the way for the introduction of the kingdom of the Messiah. However, it will not follow from this that Christian baptism is now ever to be repeated.

For this, there is no warrant, no example in the New Testament. There is no command to repeat it, as in the case of the Lord's Supper; and the nature and design of the ordinance evidently supposes that it is to be performed only once. The disciples of John were rebaptized, not because baptism is designed to be repeated, but because they had never, in fact, been baptized in the manner prescribed by the Lord Jesus.

In the name of the Lord Jesus. See Barnes on Acts 2:38.

Note the prepositions "Unto" or "into" in connection with the phrase name of the Lord Jesus; compare 1 Corinthians 1:13.