We would like to be mindful of those that have yet to receive the full understanding of baptism. I, personally, do not believe I know it all. But I have studied baptism and can conclude that the name that we must be baptized in, is only held by one.
The common view held by many Christians claims that this verse:
Matthew 28:19 NKJV
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,
Means to go baptize saying “I baptize you in the name of the Father, in the name of the Son, and in the name of the Holy Spirit.”
Fact #1: Matthew 28:19 is viewed by Biblical scholars as not being an authentic saying of Jesus. Instead, the writer, Matthew, could have summed up his understanding of who Jesus was, or, was a later addition that we should not build doctrine on. Since this verse does appear in the earliest manuscripts, one must consider that Matthew decided to point to who Jesus was. (Matthew’s audience were Jewish, if I recall correctly, which would make sense if he was tying the Old Testament to Jesus.)
Fact #2: No one was ever baptized in the 1st century using the formula only found within the 2nd century. All previous baptisms were done in:
Acts 2:38,41 NKJV
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.  Then those who gladly received his word were baptized; and that day about three thousand souls were added to them.
Acts 10:47-48 NKJV
“Can anyone forbid water, that these should not be baptized who have received the Holy Spirit just as we have?”  And he commanded them to be baptized in the name of the Lord. Then they asked him to stay a few days.
Acts 19:4-5 NKJV
Then Paul said, “John indeed baptized with a baptism of repentance, saying to the people that they should believe on Him who would come after him, that is, on Christ Jesus.”  When they heard this, they were baptized in the name of the Lord Jesus.
Acts 22:16 NKJV
And now why are you waiting? Arise and be baptized, and wash away your sins, calling on the name of the Lord.’
1 Corinthians 1:12-13 NKJV
Now I say this, that each of you says, “I am of Paul,” or “I am of Apollos,” or “I am of Cephas,” or “I am of Christ.”  Is Christ divided? Was Paul crucified for you? Or were you baptized in the name of Paul?
As you can see, the early Church baptized only in the name of Jesus (or Yeshua in Aramaic).
But what about the name? Well, let’s see, Jesus:
John 5:43 NKJV
I have come in My Father’s name, and you do not receive Me; if another comes in his own name, him you will receive.
Matthew 24:5 NKJV
For many will come in My name, saying, ‘I am the Christ,’ and will deceive many.
John 14:26-28 NKJV
But the Helper, the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all things that I said to you.  Peace I leave with you, My peace I give to you; not as the world gives do I give to you. Let not your heart be troubled, neither let it be afraid.  You have heard Me say to you, ‘I am going away and coming back to you.’ If you loved Me, you would rejoice because I said, ‘I am going to the Father,’ for My Father is greater than I.
So we see that all three bear the name of Jesus. Christ (Jesus’ fleshy body) did not have a name. He had the Father’s name. He bore the name of Jesus.
As for the Holy Ghost:
When we feel the presences of God, we don’t say “hey, God is here and so is the Holy Ghost!” Why not? Because that would be making two spirits of God. God is only one spirit. And His spirit is the Holy Spirit.
But as God is inactive as a Spirit, His Spirit can and will move (at least in portions) and that active force (the Holy Ghost) bears the name of Jesus.
So do you need to be baptized or even rebaptized in the name of Jesus?
Well, did you call on Jesus when you believed? Confess with your mouth? Probably, but if you were baptized, were you baptized in His name?
Maybe you want to say that the name of the Father, Son, and Holy Ghost is just a phrase. Yet, according to the Old Testament… the Father has many names. So which name? Which name for the Son? And the Holy Ghost? It clearly has a single name that Matthew was referring to. That name is Jesus.
Baptism with the formula Father, Son, and Holy Ghost was a Catholic practice. The same Roman Catholic Church that would claim you to be a heretic today!
My last words will be a question to you.
Mark 16:17-18 NKJV
And these signs will follow those who believe: In My name they will cast out demons; they will speak with new tongues;  they will take up serpents; and if they drink anything deadly, it will by no means hurt them; they will lay hands on the sick, and they will recover.”
You pray for the sick in the name of Jesus.
You cast out demons in the name of Jesus.
You pray in the name of Jesus.
You come together to worship in the name of Jesus.
Everything you do is in the name of Jesus.
But, if that is so, then why don’t you get baptized in His name?
John 14:14 NKJV
If you ask anything in My name, I will do it.
Matthew 28:18 NKJV
And Jesus came and spoke to them, saying, “All authority has been given to Me in heaven and on earth.
Acts 4:12 NKJV
Nor is there salvation in any other, for there is no other name under heaven given among men by which we must be saved.”
If the only saving name is Jesus, and Jesus said to get baptized, and his disciples baptized in his name, why aren’t you baptized in his name?