I think you are reading into this what you want to.
I have quoted some in red as you quoted. The others seem a bit clearer to me. This does not show that they all have the same name GOD.
This show that they are being baptized by the three things that are important. The father (GOD), the Son who God sent to save us, And the Holy Spirit that God uses to help us. He is telling them to Baptize in the three names because this is part of the new convenant. It is recognizing that the son is needed for our salvation and we need the Holy Spirit to help. It is NOT making a statement that they are one GOD.
How you come to the conclusion that this means they are One really stretches the imagination.
New International Version(©1984)
Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,
New Living Translation(©2007)
Therefore, go and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit.
English Standard Version(©2001)
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,
New American Standard Bible(©1995)
"Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit,
International Standard Version(©2008)
Therefore, as you go, disciple people in all nations, baptizing them in the name of the Father, and the Son, and the Holy Spirit,
GOD'S WORD® Translation(©1995)
So wherever you go, make disciples of all nations: Baptize them in the name of the Father, and of the Son, and of the Holy Spirit.