Just fyi, I've thought a lot about this subject and since scripture can't and doesn't conflict with or contradict scripture, nor dies scripture supersedeother scripture, I've concluded that both Matthew 28:19 and Acts 2:38 have to be right; and per your question regarding what is the name of God and the Holy Ghost, we don't know the names. So how is this rectified? My conclusion is, if both are correct and acceptable, what they both are really saying is, that it's by the authority of either the father and of the Son and of the Holy Ghost, or Jesus Christ, and naming names is not necessary. It's by the authority of, much like saying today, by the authority of the queen or king, etc. And if you look closely at the examples of immersions, nothing was actually said by the one baptizing another, nor is there anything scripturally required of anything actually to be said prior to immersion by the baptizer. Only the one being baptized is required to say anything as did the Ethiopian eunuch in Acts 8, wherein it's recorded the eunuch confessed his belief in Jesus Christ. This is also consistent with Romans 10:9-10, and further evidenced by what Saul was told to do in Acts 22:16, "calling on the name of the Lord". Just my opinion and observation.
I will start this out with a very clear scripture.
1 Timothy 3:16 And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory.
I understand, what does HIS word say we are to do when we ask for anything?
There has to be an explanation.
John 14:13-14
13 And
whatsoever ye shall ask
in my name, that will I do, that the Father may be glorified in the Son.
14 If ye shall ask any thing
in my name, I will do it.
John 16:24 - Hitherto have ye asked nothing
in my name: ask, and ye shall receive, that your joy may be full.
No where, will you see that in the titles of JESUS.
In Matthew 28:19 JESUS is speaking to HIS disciples who knew who HE was.
John 14:6 Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.
7 If ye had known me, ye should have known my Father also: and from henceforth ye know him, and have seen him.
8 Philip saith unto him, Lord, show us the Father, and it sufficeth us.
9 Jesus saith unto him, Have I been so long time with you, and yet hast thou not known me, Philip? he that hath seen me hath seen the Father; and how sayest thou then, Show us the Father?
10 Believest thou not that I am in the Father, and the Father in me? the words that I speak unto you I speak not of myself: but the Father that dwelleth in me, he doeth the works.
11 Believe me that I am in the Father, and the Father in me: or else believe me for the very works' sake.
So HIS disciples knew who HE was, did they disobey HIM when JESUS told them,
Matthew 28:18-19
18 And Jesus came and spake unto them, saying,
All power is given unto me in heaven and in earth.
19 Go ye therefore, and teach all nations, baptizing them
in the name of the Father, and of the Son, and of the Holy Ghost:
What is "
THE NAME OF"
Notice in verse 18 "All power is given unto me in heaven and in earth."
HIS disciples knew who HE was and OBEYED what HE told them to do.
look at this verse, John 3:13 And no man hath ascended up to heaven, but he that came down from heaven,
even the Son of man which is in heaven.
JESUS speaking while HES here on earth BUT HE'S IN HEAVEN ALSO.
HIS word is deep, we need to put all of the piece together and if they don't fit we are the one that is wrong.
In the year 325 the forerunners of the catholic church invented the trinity and if you didn't agree with they you were put to death.
So many people follow it today.
In Romans 10, if you read the whole chapter you will see Paul is speaking to one of the churches he started and he is telling his church to get out and preach, confess JESUS and they shall be saved.
He is not taking to the lost, but those who have been reborn proving that once saved always saved is not true.
In every recorded act of baptism it was done in JESUS name so what are we to do?
GOD BLESS you in your walk, we will NEVER know it all but need to stay humble.