Our tract on Baptism states:
Rather, the phrase “baptized in the name of Jesus” is simply Luke’s way to distinguish Christian baptism from other baptisms of the period, such as John’s baptism (which Luke mentions in Acts 1:5, 22, 10:37, 11:16, 13:24, 18:25, 19:4), Jewish proselyte baptism, and the baptisms of pagan cults (such as Mithraism). It also indicates the person into whose Mystical Body baptism incorporates us (Rom. 6:3).
The early Church Fathers, of course, agreed. As the following quotes illustrate, Christians have from the beginning recognized that the correct form of baptism requires one to baptize “in the name of the Father and of the Son and of the Holy Spirit.”
“After the foregoing instructions, baptize in the name of the Father, and of the Son, and of the Holy Spirit, in living [running] water. If you have no living water, then baptize in other water, and if you are not able in cold, then in warm. If you have neither, pour water three times on the head, in the name of the Father, and of the Son, and of the Holy Spirit. Before baptism, let the one baptizing and the one to be baptized fast, as also any others who are able. Command the one who is to be baptized to fast beforehand for one or two days” (Didache 7:1 [A.D. 70]).
For the rest of the tract, see: catholic.com/tracts/trinitarian-baptism
Fr. Vincent Serpa, O.P.