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It appears to me that you missed the main point about the Jesus name baptism. Jesus commanded that his disciples be baptized in the "name" of someone. Who do you suppose he meant that name to be? He didn't say (about Matthew 28:19) "repeat after me now". Do you suppose that after hearing Matthew 28:19 they got together and decided to disobey Christ? Of course not! They obeyed Him and directly fulfilled Matthew 28:19 because they knew who Christ was, He was and is the image of the invisible God and the fullness of the godhead bodily. The correct baptism has to be in the name of the testator who is Jesus Christ. There is no other name. By the way, where is the name of the Father and Holy Ghost in the New Testament? Jesus declared in the book of John that he had "declared thy name" to His disciples. Whose name did He declare?
You concluded correctly that Matthew 28:19 is not a formula required to be said during a baptism. "Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, "teaching them to observe all things that I have commanded you; and lo, I am with you always, even to the end of the age." Amen" (Matthew 28:19-20). For exactly the same reason, verses such as Acts 2:38, which says "Then Peter said to them, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit," are not a formula either.
However, you failed to understand the meaning of "in the name of."
The phrase "in the name of" means "by the authority of" or "with the approval of." We use the phrase in the same sense when the police man commands, "Stop in the name of the law!" The order to halt does not come by the police man's personal will but by the authority the law grants to the officer. When a person is baptized in the name of Jesus, it is a statement that the baptism was not authorized by any man but is done at the expressed command of Christ. But even Jesus stated that his authority is not his own. All that he has was received from the Father. "For I have come down from heaven, not to do My own will, but the will of Him who sent Me" (John 6:38). Hence, anything done by the authority of Christ is done by the authority of God the Father. In addition, look back once again at John 16:13 and you will see that the Holy Spirit also did not act of his own authority. Jesus said of the Spirit, "He will glorify Me, for He will take of what is Mine and declare it to you" (John 16:14). Therefore, anything done by the authority of the Spirit is also done by the authority of Christ. Such should not surprise anyone. Our God is one! To be baptized in the name of the Father, and of the Son, and of the Spirit is exactly the same as being baptized in the name of the Son.
When the Peter stated, "Nor is there salvation in any other, for there is no other name under heaven given among men by which we must be saved" (Acts 4:12), he stated the same thing that Jesus said in Matthew 28:18: "And Jesus came and spoke to them, saying, "All authority has been given to Me in heaven and on earth."" Jesus currently holds all authority, both in heaven and on earth. Therefore, salvation cannot come by any other authority (or in the name of any other). Yet the authority that Jesus holds is that granted by the Father. "For "He has put all things under His feet." But when He says "all things are put under Him," it is evident that He who put all things under Him is excepted. Now when all things are made subject to Him, then the Son Himself will also be subject to Him who put all things under Him, that God may be all in all" (I Corinthians 15:27-28). In other words, the supreme authority that Jesus wields is the authority of the Father. Hence, baptism in the name of Jesus (under the authority granted by Jesus) is in the name of the Father (under the authority granted by the Father). That is why Jesus said, "I am the way, the truth, and the life. No one comes to the Father except through Me" (John 14:6).
The answer to your last question is found in John 17:25-26, "O righteous Father! The world has not known You, but I have known You; and these have known that You sent Me. And I have declared to them Your name, and will declare it, that the love with which You loved Me may be in them, and I in them." The name Jesus declared is the name of His righteous Father.
See also:
Questions
and Answers regarding God
Questions and Answers regarding
the Godhead
Questions and Answers regarding
Trinity