There’s a good article on this subject right here at CAF entitled
Trinitarian Baptism which corresponds quite accurately to this question.
It quotes the early Church Fathers who "*agreed… 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.’ " *
As to the question raised by the OP, the most pertinent section of the article replies (blue bolds and smiley mine):
*" ‘Jesus Only’ Pentecostals also argue that the New Testament talks about people being baptized “in the name of Jesus,” but there are only four such passages (Acts 2:38, 8:16, 10:48, and 19:5). Further, these passages do not use the same designation in each place (some say “Lord Jesus,” other say “Jesus Christ”), indicating that they were not technical formulas used in the baptism but simply descriptions by Luke. **These four descriptions are not to be considered - :tsktsk: - as a substitute for or contradiction of the divine command *
of the Lord Jesus Christ to: “make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit” (Matt. 28:19). "
So, we may rightly ask : Then if “in the name of Jesus”,“Lord Jesus” and “Jesus Christ” are not Baptismal formulas, but rather descriptions, what are they describing ?
One could say they are a reference to by Whose authority precisely we baptize. The verse of scripture which directly precedes the wording of the baptismal formula bears this out. Here are the two verses in context of each other- the way they appear in the bible :
**Matt 28: 18-19 **
Then Jesus approached and said to them, "All power in heaven and on earth has been given to me.
Go, therefore, and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the holy Spirit,
Final note: the linked article also bears the following-
both the
*"NIHIL OBSTAT: I have concluded that the materials
presented in this work are free of doctrinal or moral errors.
Bernadeane Carr, STL, Censor Librorum, August 10, 2004 *
(and)
*IMPRIMATUR: In accord with 1983 CIC 827
permission to publish this work is hereby granted.
+Robert H. Brom, Bishop of San Diego, August 10, 2004" *
