In a recent work on evaluating Roman Catholic doctrine (which I recommend, for those interested), Catholic apologist Jimmy Akin discussed the debate about baptism “in Jesus’ name”:
The Validity of Baptism “in Jesus’ Name”
549. Based on Matthew 28:19, the Church baptizes using the trinitarian formula “in the name of the Father, and of the Son, and of the Holy Spirit.” However, in the New Testament we also read of baptism being administered “in the name of Jesus Christ” (Acts 2:38; 10:48), “in the name of the Lord” (Acts 8:16), and “in the name of the Lord Jesus” (Acts 19:5). This raises the question of whether such formulas were actually used in the early Church or whether they are a shorthand way of referring to Christian baptism (as opposed to John’s baptism and Jewish ritual washings)—the full trinitarian formula being too long to give on each occasion.
If baptism were administered using a formula like “in Jesus’ name,” without denying the doctrine of the Trinity, would it be valid? The Magisterium hasn’t dealt with this question in recent times, and the statements of prior popes are mixed. In 256, Pope Steven I apparently referred to both formulas without deciding between them (DH 111), In 404, Pope Innocent I referred to being baptized “in the name of Christ” without condemning it or indicating it was to be understood as shorthand (DH 211). Around 558, Pope Pelagius I stated failure to use the trinitarian formula would invalidate baptism (DH 45). But in 866, Pope Nicholas I cited the precedent of Acts and the opinion of St. Ambrose to indicate that baptism “in the name of the Holy Trinity or only in the name of Christ” would be valid (DH 646). Ludwig Ott concludes: “The Church has pronounced no final decision on the question” (Fundamentals of Catholic Dogma, pp. 353-54).
It is noteworthy that when the Catechism addresses the issue, it doesn’t discuss formulas like “in Jesus’ name.” Neither does it say the essential form of baptism is the trinitarian formula. It merely says that the trinitarian formula is used, in slightly different forms, in the Latin and Eastern liturgies (CCC 1240). In light of the prior mixed doctrinal tradition on this question, this illustrates why the hermeneutic of precision is important and why we need to consider what magisterial documents are not saying. (Jimmy Akin, Teaching with Authority: How to Cut Through Doctrinal Confusion and Understand What the Church Really Says [El Cajon, Calif.: Catholic Answers Press, 2018], 331-32)
While Akin is not guilty of such claims, many Catholic apologists often claim that, due to the purported infallibility of the extraordinary magisterium (ex cathedra statements from the Pope and general councils) and the ordinary magisterium, as well as the concept of “secondary objects of infallibility,” there is little or no doctrinal confusion. Notwithstanding such errant claims, here we have a long-standing (centuries [!] of debate) about a key soteriological issue. Rome correctly holds to baptismal regeneration, but the “form” of baptism (i.e., the formula/wording used) must be a proper one to confect the sacrament and its purpose. If one is baptised “in Jesus’ name” but such baptism is invalid, one must be baptised again (unconditionally, too) as they never received a “true” baptism, and thus, are not regenerated, justified, and been adopted a son/daughter of God, but if one does not receive baptism (even conditional baptism), they are spiritually dead, and any sacraments they receive (e.g., confirmation) are not validly received, and in the case of the Eucharist, eating and drinking condemnation to their souls (cf. 1 Cor 11:29).