Critics have found some difficulty in reconciling this shorter baptism formula, "In the Name of the Son," with the formula given by Matthew (28:19), "In the Name of the Father and of the Son and of the Holy Ghost."
In defense it has been replied that baptism in the first church was administered "in the name of Christ," meaning, by his authority, "for" him; but "into the name of the Trinity," or, into the communion with the Tri-une Godhead. It has been said that the use by the authors of the New Testament of two different particles Acts 19:4). Luke here uses the formula of Matthew, as far as the particle "into" is concerned. The inference is fair that the briefer formula, "in the name of Jesus" is the same as the longer formula, only abbreviated, but meaning the same. That, in other words, baptism in the name, or into the name, of Jesus, means in the New Testament, as here, baptism both "in" and "into" the name of the Godhead. (See vv. 12 and 13; also 21)