The introduction and unit study should be read prior to this.

Baptism is a ceremony where water is used and through this water a person becomes a member of a “Christian church” (Christ body).
Baptism is a signal of regretness and forgiveness – Ac 2.38 -  and union with Christ – Ga 3.26-27 -  in His death as well as in His resurrection – Ro 6:3-5 – Baptism is also, according to dictionary, an act of giving a name to a person or thing

The wish of baptism comes with the knowledge and faith in the scriptures that show we have to become sons of God, that means we have to be Jesus and be part of His body. Being Jesus, we become sons and being sons, we have the inheritance, that is everlasting life.
Mark 16:16 He who believes and is baptized will be saved; but he who does not believe will be condemned.

The baptism nowadays are not correct, are not according to the bible as the name Jesus is not given and they only repeat what was said by Jesus in Matthew 28:19  "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”

The example below clarifies it:

John Smith asks his son Peter: “go to the bank and in my name ask the managers to give you my documents. So Peter goes to the bank and tells the manager: “I am here in the name of my father that asked you to give me his documents”. Probably the manager would ask: “What is your father’s name?” and Peter would say “John Smith”.
Notice that it is necessary the existence of a name for the delivery of the documents. The same happens with baptism where you are recognized by God only after receiving the name “Jesus”.

When Jesus said to have baptism in the name of “Father, Son and Holy Spirit”, the  apostles ( notice here they were full of Holy Spirit, what means the same spirit of Jesus which does not deceive or contradict ) did exactly what He said, putting the name of “Father, Son and Holy Spirit” that is JESUS. All the baptisms made in the bible are in the name of Jesus.
When we talk about baptism in the name of Jesus, many people, almost everybody, tell that the ones who act like this belong to a sect and that it must no be followed. This is an absurd!
The baptism of Jesus is an example of how we become sons of God. Notice that act is an example for us so that when we are baptized, we feel that God recognizes us as His sons (this is my beloved son…). And together with baptism we receive the Holy Spirit.
Everything Jesus did was an example of how we must behave and what must be followed and it is the same for baptism. In the passage 1Peter 2:21 we see that:

For to this you were called, because Christ also suffered for us, leaving us an example, that you should follow His steps:
In the next passage, John did not understand the reason why Jesus had asked him to be baptized as he recognized who Jesus really was. But Jesus did that as an example to be followed by us who want to become sons:Matthew 3:13 Then Jesus came from Galilee to John at the Jordan to be baptized by him.
14 And John tried to prevent Him, saying, "I need to be baptized by you, and are you coming to me?"15 But Jesus answered and said to him, "Permit it to be so now, for thus it is fitting for us to fulfill all righteousness." Then he allowed Him.
16 When He had been baptized, Jesus came up immediately from the water; and behold, the heavens were opened to Him, and He saw the Spirit of God descending like a dove and alighting upon Him.17 And suddenly a voice came from heaven, saying, "This is my beloved Son, in whom I am well pleased."

This passage testifies that, after being baptized, the believer becomes the beloved son of God and also receives the Holy Spirit. If this demonstration had not existed (the voice from the sky and the symbol of the Holy Spirit as a dove) its comprehension would have been difficult.

How to baptize:

“In the name of Lord Jesus I baptize you (here, the name of the person) with the name of Jesus Christ”

In order to explain the first part (in the name of Lord Jesus), let us analyze what Colossians 3:17 says: And whatever you do in word or deed, do all in the name of the Lord Jesus, giving thanks to God the Father through Him.

Obviously the second Jesus that appears in the sentence is the new name of the baptized person.

Below we see what the scriptures tell about baptism:

Does not act 4:12 “Nor is there salvation in any other, for there is no other name under heaven given among men by which we must be saved."
1Peter 3:21 There is also an antitype which now saves us——baptism

Below we see more passages about baptism and unity

Matthew 28:19 “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,

Matthew 1:18 ¶ Now the birth of Jesus Christ was as follows: After His mother Mary was betrothed to Joseph, before they came together, she was found with child of the Holy Spirit.

20 But while he thought about these things, behold, an angel of the Lord appeared to him in a dream, saying, "Joseph, son of David, do not be afraid to take to you Mary your wife, for that which is conceived in her is of the Holy Spirit.
21  "And she will bring forth a Son, and you shall call His name JESUS, for He will save His people from their sins."

Acts 20:28 "Therefore take heed to yourselves and to all the flock, among which the Holy Spirit has made you overseers, to shepherd the church of God which He purchased with His own blood.

John 14:8 Philip said to Him, "Lord, show us the Father, and it is sufficient for us."
9  Jesus said to him, "Have I been with you so long, and yet you have not known Me, Philip? He who has seen Me has seen the Father; so how can you say, ‘Show us the Father’?

John 10:30 “I and My Father are one."

1 John 5:20  And we know that the Son of God has come and has given us an understanding, that we may know Him who is true; and we are in Him who is true, in His Son Jesus Christ. This is the true God and eternal life.

John 17:11 ¶ "Now I am no longer in the world, but these are in the world, and I come to you. Holy Father, keep through your name those whom you have given me that they may be one as we are.
12 “While I was with them in the world, I kept them in your name. Those whom you gave me I have kept; and none of them is lost except the son of perdition, that the Scripture might be fulfilled.

Acts 19:1 ¶ And it happened, while Apollos was at Corinth, that Paul, having passed through the upper regions, came to Ephesus. And finding some disciples
2  he said to them, "Did you receive the Holy Spirit when you believed?" So they said to him, "We have not so much as heard whether there is a Holy Spirit."
3  And he said to them, "Into what then were you baptized?" So they said, "Into John’s baptism."
4  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."
5  When they heard this, they were baptized in the name of the Lord Jesus.
6  And when Paul had laid hands on them, the Holy Spirit came upon them, and they spoke with tongues and prophesied.

Ephesians 4:4  There is one body and one Spirit, just as you were called in one hope of your calling;
5  one Lord, one faith, one baptism;
6  one God and Father of all, who is above all, and through all, and in you all.

Ezekiel 39:29  ‘And I will not hide My face from them anymore; for I shall have poured out My Spirit on the house of Israel,’ says the Lord GOD."

Joel 2:28 ¶ "And it shall come to pass afterward That I will pour out My Spirit on all flesh; Your sons and your daughters shall prophesy, Your old men shall dream dreams, Your young men shall see visions.
29  And also on My menservants and on My maidservants I will pour out My Spirit in those days.

Zachariah 14: 9  And the LORD shall be King over all the earth. In that day it shall be—"The LORD is one," And His name one.

Colossians 3:17  And whatever you do in word or deed, do all in the name of the Lord Jesus, giving thanks to God the Father through Him.

Mark 16:15  And He said to them, "Go into all the world and preach the gospel to every creature.
16  "He who believes and is baptized will be saved; but he who does not believe will be condemned.
17  "And these signs will follow those who believe: In My name they will cast out demons; they will speak with new tongues;
18  "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."
19 ¶ So then, after the Lord had spoken to them, He was received up into heaven, and sat down at the right hand of God.

Luke 24:45  And He opened their understanding, that they might comprehend the Scriptures.
46  Then He said to them, "Thus it is written, and thus it was necessary for the Christ to suffer and to rise from the dead the third day,
47  "and that repentance and remission of sins should be preached in His name to all nations, beginning at Jerusalem.
48  "And you are witnesses of these things.
49  "Behold, I send the Promise of My Father upon you; but tarry in the city of Jerusalem until you are endued with power from on high."

Acts 8:12  But when they believed Philip as he preached the things concerning the kingdom of God and the name of Jesus Christ, both men and women were baptized.
13  Then Simon himself also believed; and when he was baptized he continued with Philip, and was amazed, seeing the miracles and signs which were done.
14 ¶ Now when the apostles who were at Jerusalem heard that Samaria had received the word of God, they sent Peter and John to them,
15  who, when they had come down, prayed for them that they might receive the Holy Spirit.
16  For as yet He had fallen upon none of them. They had only been baptized in the name of the Lord Jesus.
17  Then they laid hands on them, and they received the Holy Spirit.

Acts 2:1 ¶ When the Day of Pentecost had fully come, they were all with one accord in one place.
2  And suddenly there came a sound from heaven, as of a rushing mighty wind, and it filled the whole house where they were sitting.
3  Then there appeared to them divided tongues, as of fire, and one sat upon each of them.
4  And they were all filled with the Holy Spirit and began to speak with other tongues, as the Spirit gave them utterance.

Acts 2:38  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.
Galatians 3:26  For you are all sons of God through faith in Christ Jesus.
27  For as many of you as were baptized into Christ have put on Christ.

Romans 6:3 Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death?
4  Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life.
5  For if we have been united together in the likeness of His death, certainly we also shall be in the likeness of His resurrection,