This is what Peter taught on the Day of Pentecost, when the disciples actually began to fulfill Christ's commandment to "teach all nations:"
ACTS 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
The Name of Jesus Christ was a consistent part of what Peter taught:
ACTS 4:10 Be it known unto you all, and to all the people of Israel, that by the name of Jesus Christ of Nazareth, whom ye crucified, whom God raised from the dead, even by him doth this man stand here before you whole.
ACTS 4:11 This is the stone which was set at nought of you builders, which is become the head of the corner.
ACTS 4:12 Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.
Peter, being one of the eleven, was a chosen witness of not only suffering and resurrection of Jesus Christ, but also of the message of 1) repentance, and 2) remission of sins being preached in the name of Jesus Christ (per Luke 24:45-48)!! Jesus Himself said:
MATTHEW 28:19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
At Acts 2:38, Peter understood what Jesus meant when He said Matthew 28:19. (We must remember that Peter was there on the day of Pentecost—we were not. Jesus chose Peter (and the other apostles) to teach us the ways of the Lord. And what did they teach, where names are concerned? First, we can re-read Acts 2:38 and Acts 4:10-12 again (as quoted above). In addition, we should observe that the word "trinity" is never in the Bible-not even once! Furthermore, it should be noted that nowhere in the bible was anyone ever baptized, saying, "in the name of the Father, and of the Son, and of the Holy Ghost"—not even once!
What the Apostles did is recorded in the book of Acts (which is why that book is properly called "The Acts of the Apostles"). If the words "In the name of the Father, and of the Son, and of the Holy Ghost" were used in any context in the book of Acts (including baptism), then it would be mentioned, at least somewhere. (Ordinarily, "word-counting Bible studies" are of little value, but in this instance it may be necessary in order to punctuate this point.)
The word "Father" is part of the phrase "in the name of the Father, and of the Son, and of the Holy Ghost." A complete list of every instance of the word "father" in the Book of Acts can be found in Strongs Exhaustive Concordance, Complete and Unabridged, Compact Edition, by James H. Strong, Baker Book House, Grand Rapids, concordance p. 338. What follows is a complete list of each time the word "father" as used in the Book of Acts:
That's all! That's every instance of the word "father" in the book of Acts. The phrase "In the name of the Father, and of the Son, and of the Holy Ghost" is not in the book of Acts; Nobody was ever baptized in these titles, nor by saying anything about a trinity.
Christ's command at Matthew 28:19 was obeyed, because Peter understood that the name of the Father, and of the Son, and of the Holy Ghost is "Jesus Christ!!" (Just as the name of the first President, and of the first Commander–in–chief, and of the first Chief Executive, etc., is "George Washington," for example. )
In previous Bible Studies, we discussed at great length that God had indeed come to the earth in the Old Testament in various different forms (manifestations), and we pointed out that God had come in the form of a man on no less than five (5) previous occasions. For more information on this topic, please refer to the Bible study series on the Godhead.