I always wondered about Matthew 28:19, so as I like to do, I studied it out.
The rest of the Bible does not perfectly line up with this scripture, and we have to use the whole Bible to determine what is truth.
For example: Every record of baptism in the book of Acts shows that the Apostles obeyed His command by baptizing in the name of Jesus, or in the name of the Lord (Jesus).
Would the Apostles have disobeyed Him? God forbid! Think about this. There is NO WAY that the Apostles would have disobeyed Jesus.
Here's a few scripture references showing baptism in the name of the Lord Jesus: Acts 2:38, Acts 8:16, Acts 10:48, Acts 19:5, Acts 22:16, Rom 6:3, Gal 3:27, Col 2:12, 1 Pet 3:21
That's the first test.
The second is; did "they", the interpreters of the Bible back in the first few centuries, change it to agree with what they believed? Like 1 John 5:7, where it is common knowledge that words were inserted that were not in the original text, (Click here to see a screenshot of Strongs Greek/Hebrew dictionary) did they insert words to make the scripture agree with what they thought was true?
I invite you to read the following references on the subject:
These facts prove that the original Matthew 28:19 did not say, "in the name of the Father, Son and Holy Ghost", but in fact lines up with the rest of the scriptures very well with the words, "in My name".
Since we know that words were inserted in 1 John 5, it's a short step to understand that these words were also inserted as well.
God bless you on your quest for Truth. I pray the Lord leads you to it!