Most modern English bible translations read:

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, ... - Matthew 28:19 (ESV)

No support as a baptism formula

There are no other scripture to support Matthew 28:19 as a baptism formula. The apostles always baptized believers in the name of Jesus only, for example:

And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit.” -- Acts 2:38 (ESV)

They had only been baptized in the name of the Lord Jesus. -- Acts 8:16 (ESV)

And he commanded them to be baptized in the name of Jesus Christ. -- Acts 10:46 (ESV)

On hearing this, they were baptized in the name of the Lord Jesus. And when Paul had laid his hands on them, the Holy Spirit came on them, and they began speaking in tongues and prophesying. -- Acts 19:5 (ESV)

And he said, ‘The God of our fathers appointed you to know his will, to see the Righteous One and to hear a voice from his mouth; for you will be a witness for him to everyone of what you have seen and heard. And now why do you wait? Rise and be baptized and wash away your sins, calling on his name.’ -- Acts 22:14-16

For as many of you as were baptized into Christ have put on Christ. -- Galatians 3:27 (ESV)

Cross-references of Matthew 28:19

A cross-reference of the same verse excludes the trinity formula:

“And that repentance and remission of sins should be preached in his [Jesus] name among all nations, beginning at Jerusalem” -- Luke 24:47

Luke omits to mention the name of the Father and the Holy Spirit.

And while staying with them he [Jesus] ordered them not to depart from Jerusalem, but to wait for the promise of the Father, which, he said, “you heard from me; for John baptized with water, but you will be baptized with the Holy Spirit not many days from now.”

So when they had come together, they asked him, “Lord, will you at this time restore the kingdom to Israel?”
He said to them, “It is not for you to know times or seasons that the Father has fixed by his own authority. But you will receive power when the Holy Spirit has come upon you, and you will be my witnesses in Jerusalem and in all Judea and Samaria, and to the end of the earth.”

-- Acts 1:4-8

Jesus does not declare "you will be witnesses to the Holy Trinity".

The following verses omit "the name of the Father" and "the name of the Holy Spirit".

“And many other signs truly did Jesus in the presence of his disciples, which are not written in this book: But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name” -- John 20:30-31

“These things have I written unto you that believe on the name of the Son of God; that ye may know that ye have eternal life” -- 1 John 5:13

Validity of Matthew 28:19

The Greek Christian Justin Martyr, who wrote in the middle of the second century, never quoted “in the name of the Father, and of the Son, and of the Holy Ghost,” nor did Aphraates (Aphrahat The Persian Sage) in the early fourth century, neither the great theologian Origen, nor Hermas the shepherd. -- https://7th-day.info/great-commission-of-matthew-2819-20/

Some scholars question this verse's validity based on two factors:

1. they are not quoted by some early Church Fathers (notably Eusebius), and
2. they seem to contradict other sections of Scripture, when not properly understood.

This argument was first put forth by the nineteenth century Biblical scholar, F. C. Conybeare (1856-1924).

...

"We now have the Hebrew Matthew Gospel, a manuscript that was preserved by the Jews from the first century. In this Shem Tov MS, the text at Matthew 28:19 does not contain the Trinitarian statement."

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-- Mark Clarke

ljthriepland also points out:

In fact the Greek word translated as name in Matthew 28:19 is ὄνομα onoma, and this is in the singular form in this verse. The verse does not say in the NAMES of the father, son and Holy Ghost but name as in one name. The in the singular name of the father son and Holy Ghost. The singular name of the triune God however, if the triune God were correct would not be Jesus but YHWH.

However, it is important to note that these quotes are not reliable sources too as Mark Clarke conclude:

So the problems, which seem to demand a forsaking of all known manuscripts in favor of loosely paraphrased references in Eusebius, all disappear when one realizes that Matthew 28:19 was not meant to be a formula, but simply a description of what the new disciples would be baptized into. The Jews knew of the Father, and were aware of the workings of the holy spirit, but the identification of Jesus as the Son of God was now crucial to their baptism. Gentiles, on the other hand, may or may not have known God as a Father, or His holy spirit working in the world, and would need to be introduced into that knowledge as well as that of Christ. This would be a reasonable description of the Commission to preach and teach to “all nations.” All three, God, Jesus, and the holy spirit (which is also called the spirit of Christ) are instrumental in the entire plan of salvation. Thus being baptized as a response to the Gospel can certainly be described as being baptized “in the name of the Father, and of the Son, and of the holy spirit,” since there is no reference in that verse to the Trinitarian concepts of coequality, coexistence, or triune persons. The words of the Great Commission were in fact turned into a Trinitarian baptismal formula in later years, but there is nothing to indicate that this was the original meaning or intent of the phrase.

Missing Trinity Definition

Even if Matthew 28:19 is 100% correctly translated and does include "the name of the Father and of the Son and of the Holy Spirit", it still does not proof that they are 3 components of the Godhead or define the Trinity.

Confusing identity with authority

In English the "word" name could mean either "identity" or "authority". Because of this some people says if the identity of the Father, the Son and the Holy Spirit is the same identity, then they think this proof that they are the same.

Jesus also did not instruct his disciples to change their names to "Jesus" or "Christ" or "Christians".

"In the name of" someone means under the authority of a superior person the servant has the right or has been ordered to do certain things.

For example when Caesar send his troops to conquer a country, they do it in the "name of Caesar" which means they have been ordered and have the support of Caesar to do so.

Review the biblical example:

And when they had set them in the midst, they inquired,

“By what power or by what name did you do this?”

Then Peter, filled with the Holy Spirit, said to them,

"Rulers of the people and elders, if we are being examined today concerning a good deed done to a crippled man, by what means this man has been healed, let it be known to all of you and to all the people of Israel that by the name of Jesus Christ of Nazareth, whom you crucified, whom God raised from the dead — by him this man is standing before you well..."

-- Acts 4:7–10 (ESV)

Conclusion

Whether the baptism formula of Matthew 28:19 is valid or not, Baptism cannot be done without:

• the Father, because he has to permit us to be adopted as His children (Psalm 68:5; Romans 8:14; Galatians 3:26; Ephesians 1:5),
• God's Son, because he reconciled us by his blood so that we could be forgiven (Matthew 26:26-28; 1 John 1:7; Acts 20:28; Colossians 1:20; Ephesians 1:7; Hebrews 9:14,22; Hebrews 10:19; Hebrews 13:12; Luke 22:20) which allows us to become a new creation (John 3:3, 2 Corinthians 5:17, 1 Peter 1:23)
• the Holy Spirit, because he gives birth (life) to our spirit (John 3:5-6; John 6:63; Titus 3:5)