In Matthew 28:19 Jesus commanded His disciples to make disciples and baptise them in the name of the Father and of the Son and of the Holy Spirit.

Mat 28:18  And Jesus came and spoke to them, saying, “All authority has been given to Me in heaven and on earth.
Mat 28:19  “Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,
Mat 28:20  “teaching them to observe all things that I have commanded you; and lo, I am with you always, even to the end of the age.” Amen.

However, there is a question over the authenticity of this verse.  Concerning the words, “baptizing them in the name of the Father, and of the Son, and of the Holy Spirit,” noted Bible scholar, E.W. Bullinger, in his Word Studies on the Holy Spirit, pages 47, 48, states:

“These words are contained in every Greek MS. [manuscript] known, and are, therefore, on documentary evidence, beyond suspicion: but yet there is one great difficulty with regard to them.  The difficulty is that the Apostles themselves never obeyed this command; and in the rest of the New Testament there is no hint as to it ever having been obeyed by anyone. Baptism was always in the name of the one person of the Lord Jesus.”

Bullinger admits that every Greek manuscript has the words “baptizing them in the name of the Father and of the Son and of the Holy Spirit” but goes on to note that there is no record of this in Scripture.  Instead, people were baptised in the name of the Lord Jesus.

Here are the scriptures relating how people were baptised.

Acts 2:38  Then Peter said to them, “Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit.

Acts 8:16  For as yet He had fallen upon none of them. They had only been baptized in the name of the Lord Jesus.

Acts 10:48  And he commanded them to be baptized in the name of the Lord. Then they asked him to stay a few days.

Acts 19:5  When they heard this, they were baptized in the name of the Lord Jesus.

Acts 22:16  ‘And now why are you waiting? Arise and be baptized, and wash away your sins, calling on the name of the Lord.’

Rom 6:3  Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death?

1 Cor 1:12  Now I say this, that each of you says, “I am of Paul,” or “I am of Apollos,” or “I am of Cephas,” or “I am of Christ.”
1 Cor 1:13  Is Christ divided? Was Paul crucified for you? Or were you baptized in the name of Paul?
1 Cor 1:14  I thank God that I baptized none of you except Crispus and Gaius,
1 Cor 1:15  lest anyone should say that I had baptized in my own name.

Gal 3:27  For as many of you as were baptized into Christ have put on Christ.

In the light of Scripture, we see baptism was never performed “in the name of the Father, and of the Son, and of the Holy Spirit,” but rather, in the name of Jesus Christ alone.

Additionally, all things are to be done in Jesus’s name, which adds support to being baptised in the name of the Lord Jesus.

Col 3:17  And whatever you do in word or deed, do all in the name of the Lord Jesus, giving thanks to God the Father through Him.

Bullinger continues in Word Studies on the Holy Spirit, p.48:

“It is difficult to suppose that there would have been this universal disregard of so clear a command, if it had ever been given; or [if] it ever really formed part of the primitive text.  It is a question, therefore, whether we have here something beyond the reach of science, or the powers of ordinary Textual Criticism.  As to the Greek MSS., there are none beyond the fourth Century [Of the fourth century, there are two: the Vaticanus and the Sinaiticus–BOTH CORRUPT. All other known Greek MSS. are from 5th Century and upward], and it seems clear that the Syrian part of the Church knew nothing of these words.”

Concerning Matthew 28:19, F. Conybeare states in the Hibbert Journal, page 105.

“Eusebius cites this text of Matthew 28:19 again and again in works written between 300-336 AD, namely in his long commentaries on the Psalms, on Isaiah, his Demonstratio Evangelica, his Theophany, … in his famous history of the Church, and in his panegyric of the emperor Constantine. I have, after a moderate search in these works of Eusebius, found eighteen citations of Matthew 28:19, and always in the following form:  “Go ye and make disciples of all nations in my name, teaching them to observe all things, whatsoever I commanded you.”

Conybeare continues:

“It is evident that this [“in My name”] was the text found by Eusebius in the very ancient codices collected fifty to a hundred and fifty years before his birth by his great predecessors. Of any other form of text [than the “in My name” reading], he had never heard and knew nothing, until he had visited Constantinople and attended the Council of Nice. Then in two controversial works, written in his extreme old age, and entitled: ‘Against Marcellus of Ancyra,’ and the other ‘About The Theology Of The Church,’ he used the common reading after Nice.”

Conybeare concludes:

“It is clear, therefore, that [of all] the MSS which Eusebius inherited from his predecessor, Pamphilus, at Caesarea in Palestine, some at least preserved the original writing, in which there was no mention either of baptism or of the words ‘Father, Son, and Holy Ghost’ [in Matthew 28:19]”

Conybeare states that 18 times when Eusebius quotes Matthew 28:19 the phrase “baptizing them in the name of the Father and of the Son and of the Holy Spirit” is omitted.  Only in twice in writings late in his life did he quote Matthew 28:19 with the phrase.

The Hibbert Journal notes that Origen quotes Matt.28:19 three times — ending the quote abruptly at “nations” each time, and

that in itself suggests that his text has been censored, and the words which followed, ‘In my Name,’ struck out.

The Encyclopedia of Religion And Ethics states

The facts are, in summary, that Eusebius quotes Matthew 28:19 twenty one times, either omitting everything between ‘nations’ and ‘teaching,’ or in the form ‘make disciples of all nations in my name,’ the latter form being the more frequent.

Conclusion

It seems the words, “baptizing them in the name of the Father, and of the Son, and of the Holy Ghost,” have been added to God’s word to support the Trinitarian doctrine, brought in by the philosophers and other pagan converts to Christianity.  It seems these words were not part of the original God-inspired text, much like the added words recorded in I John 5:7 (which are not in any Greek MS. prior to the 16th century).

In which case Mat 28:19-20 should read:

Mat 28:19 “Go therefore, and make disciples of all the nations
Mat 28:20 teaching them to observe all things that I have commanded you: and, lo, I am with you always, even to the end of the age.” Amen.

Should baptism be in the name of the Father the Son and the Holy Spirit?  In the light of what has been discussed, being bapitsed in the name of the Lord Jesus is a much safer option.