Well the name of Jesus is the only name by which anyone is saved, so it is appropriate that this is the name mentioned upon baptism.
See Acts 2…11This Jesus is ‘the stone you builders rejected, which has become the cornerstone.’ 12
Salvation exists in no one else, for there is no other name under heaven given to men by which we must be saved.”
Romans 10
But what does it say? “The word is near you; it is in your mouth and in your heart,”
d that is, the word of faith we are proclaiming:
9that if you confess with your mouth, “Jesus is Lord,” and believe in your heart that God raised Him from the dead, you will be saved.
10For with your heart you believe and are justified, and with your mouth you confess and are saved.
11It is just as the Scripture says: “Anyone who believes in Him will never be put to shame.”
e 12For there is no difference between Jew and Greek: The same Lord is Lord of all, and gives richly to all who call on Him,
13for, “Everyone who calls on the name of the Lord will be saved.”
f
Note:
Jesus is Lord
When someone is a brand new believer, they not necessarily going to discern who 'Father, Son and Holy Spirit' are, or that the Lord IS Jesus Christ.
Father could mean...their earthly dad, their own son, and holy spirit could be any old ghost! Lord could mean their landlord. God could mean any god, like Thor, or Allah or whoever. Especially if they come out of another religion. People call the Pope 'Father' when he's not actually, and some believe in Father Christmas!
You need to be specfic and mention the name above all names Jesus Christ as Lord. That is WHO we believe in.
I understand people are lazy about this and think the trinity just is self evident. Yes the trinity is important but that is a WITNESS to Jesus' name. Jesus means 'salvation'. That is why His name is important. None of us get baptised 'in the name of God'
Anyway, I always thought it was curious that ministers were lazy and did this when in the Bible, Acts 2:38 mentions Jesus name very specifically and on many other occasions.
If I see someone doing this (lazily saying 'I baptise you in the name of the Father, Son and Holy spirit' I want to shout to them YOU ARE DOING IT WRONG...don't fake baptise people! Its not about YOU (the baptiser! and how good you sound with an incantation) it's about JESUS.
And the very sad thing is...now there are so many 'believers' who think they are baptised when they were not..and that is why so many have problems with their walk. I was even fake baptised. I had to do it again properly when God reminded me that the baptism I had at 17 was church ritual baptism that had no effect! (they didn't even check if you understood the gospel back then, it was like, do you want to become a christian? Ok we're going to dunk you in the fountain).