John Gill's Bible Commentary Ver. 5. When they heard this , etc.] That is, the people to whom John preached, his hearers; when they heard of the Messiah, and that Jesus was he, and that it became them to believe in him: they were baptized in the name of the Lord Jesus ; not the disciples that Paul found at Ephesus, but the hearers of John; for these are the words of the Apostle Paul, giving an account of Johns baptism, and of the success of his ministry, showing, that his baptism was administered in the name of the Lord Jesus; and not the words of Luke the Evangelist, recording what followed upon his account of Johns baptism; for then he would have made mention of the apostles name, as he does in the next verse; and have said, when they heard this account, they were baptized by Paul in the name of the Lord Jesus: the historian reports two things, first what Paul said, which lies in ( Acts 19:4,5) then what he did, ( Acts 19:6) where he repeats his name, as was necessary; as that he laid his hands upon them, which was all that was needful to their receiving the extraordinary gifts of the Holy Ghost, having been already baptized in the name of the Lord Jesus: which sense is the more confirmed by the particles men and de , which answer to one another in verses 4 and 5, and show the words to be a continuation of the apostles speech, and not the words of the historian, which begin in the next verse. Bezas ancient copy adds, for the remission of sins.
Matthew Henry Commentary
Verses 1-7 - Paul, at Ephesus, found some religious persons, who looked to Jesus a the Messiah. They had not been led to expect the miraculous powers of the Holy Ghost, nor were they informed that the gospel was especiall the ministration of the Spirit. But they spake as ready to welcome the notice of it. Paul shows them that John never design that those he baptized should rest there, but told them that they should believe of Him who should come after him, that is, on Christ Jesus. The thankfully accepted the discovery, and were baptized in the name of the Lord Jesus. The Holy Ghost came upon them in a surprising, overpowerin manner; they spake with tongues, and prophesied, as the apostles an the first Gentile coverts did. Though we do not now expect miraculou powers, yet all who profess to be disciples of Christ, should be calle on to examine whether they have received the seal of the Holy Ghost, in his sanctifying influences, to the sincerity of their faith. Many see not to have heard that there is a Holy Ghost, and many deem all that is spoken concerning his graces and comforts, to be delusion. Of such it may properly be inquired, "Unto what, then, were ye baptized?" for the evidently know not the meaning of that outward sign on which they plac great dependence.
Greek Textus Receptus
ακουσαντες 191 5660 V-AAP-NPM δε 1161 CONJ εβαπτισθησαν 907 5681 V-API-3P εις 1519 PREP το 3588 T-ASN ονομα 3686 N-ASN του 3588 T-GSM κυριου 2962 N-GSM ιησου 2424 N-GSM
Robertson's NT Word Studies
19:5 {The name of the Lord Jesus} (to onoma ton kuriou iesou). Apollos was not rebaptized. The twelve apostles were not rebaptized. Jesus received no other baptism than that of John. The point here is simply that these twelve men were grossly ignorant of the meaning of John's baptism as regards repentance, the Messiahship of Jesus, the Holy Spirit. Hence Paul had them baptized, not so much again, as really baptized this time, in the name or on the authority of the Lord Jesus as he had himself commanded (#Mt 28:19) and as was the universal apostolic custom. Proper understanding of "Jesus" involved all the rest including the Trinity (Father, Son, and Holy Spirit). Luke does not give a formula, but simply explains that now these men had a proper object of faith (Jesus) and were now really baptized.