Against those who assert that the baptism in the name of the Father alone is sufficient.
28. Let no one be misled by the fact of the apostle's frequently omitting the name of the Father and of the Holy Spirit when making mention of baptism, or on this account imagine that the invocation of the names is not observed. “As many of you,” he says, “as were baptized into Christ have put on Christ;” and again, “As many of you as were baptized into Christ were baptized into his death.” For the naming of Christ is the confession of the whole, showing forth as it does the God who gave, the Son who received, and the Spirit who is, the unction. So we have learned from Peter, in the Acts, of “Jesus of Nazareth whom God anointed with the Holy Ghost;” and in Isaiah, “The Spirit of the Lord is upon me, because the Lord has anointed me;” and the Psalmist, “Therefore God, even your God, has anointed you with the oil of gladness above your fellows.” Scripture, however, in the case of baptism, sometimes plainly mentions the Spirit alone.
“For into one Spirit,” it says, “we were all baptized in one body.” And in harmony with this are the passages: “You shall be baptized with the Holy Ghost,” and “He shall baptize you with the Holy Ghost.” But no one on this account would be justified in calling that baptism a perfect baptism wherein only the name of the Spirit was invoked. For the tradition that has been given us by the quickening grace must remain for ever inviolate. He who redeemed our life from destruction gave us power of renewal, whereof the cause is ineffable and hidden in mystery, but bringing great salvation to our souls, so that to add or to take away anything involves manifestly a falling away from the life everlasting. If then in baptism the separation of the Spirit from the Father and the Son is perilous to the baptizer, and of no advantage to the baptized, how can the rending asunder of the Spirit from Father and from Son be safe for us? Faith and baptism are two kindred and inseparable ways of salvation: faith is perfected through baptism, baptism is established through faith, and both are completed by the same names. For as we believe in the Father and the Son and the Holy Ghost, so are we also baptized in the name of the Father and of the Son and of the Holy Ghost; first comes the confession, introducing us to salvation, and baptism follows, setting the seal upon our assent.
Source: De Spiritu Sancto (New Advent)