The baptism in Jesus name is the baptism that he has given us. Is the name of the One that can baptise us with the Holy Spirit and fire (Matthew 3:11; Mark 1:8; Luke 3:16; John 1:33; Acts 1:5 and Acts 11:16). In that name we should get baptise just like Peter said.
Peter replied, “Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit. Acts 2:38
But how do we do that? How can the Holy Spirit baptise in the Name of Jesus? Well we simply ask for it in His Name.
If you, then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give good gifts to those who ask him! Matthew 7:11
If you believe, you will receive whatever you ask for in prayer.” Matthew 21:22
And I will do whatever you ask in my name, so that the Father may be glorified in the Son. You may ask me for anything in my name, and I will do it. John 14:13-14
and so that whatever you ask in my name the Father will give you. John 15:16
In that day you will no longer ask me anything. Very truly I tell you, my Father will give you whatever you ask in my name John 16:23
In that day you will ask in my name. I am not saying that I will ask the Father on your behalf. John 16:26
The bible tells us to ask the Father in His Name and he will grant us what we ask for including the Holy Spirit.
If you then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give the Holy Spirit to those who ask him!” Luke 11:13
But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you. John 14:26
In the Name of Jesus the Holy Spirit will baptise us.
And that is what some of you were. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God. 1 Corinthians 6:11
There are examples in the bible of getting baptised by the Holy Spirit in the Name of Jesus.
On hearing this, they were baptized in the name of the Lord Jesus. When Paul placed his hands on them, the Holy Spirit came on them, and they spoke in tongues and prophesied. Acts 19:5-6
And now what are you waiting for? Get up, be baptized and wash your sins away, calling on his name.’ Acts 22:16
How do we know that this examples of baptism where Spiritually, well in Acts 19:6 it says there that received one of the gifts by the Holy Spirit which was to speak in tongues. Acts 22:16 was baptism of the Holy Spirit because the only baptism that can clean us from our sin is the baptism of the Holy Spirit. Titus 3:5 tells us that through Jesus we have been washed, regenarated and renovated by the Holy Spirit.
and repentance and forgiveness of sins will be preached in his name to all nations, beginning at Jerusalem. Luke 24:47
God exalted him to his own right hand as Prince and Savior that he might give repentance and forgiveness of sins to Israel. Acts 5:31
All the prophets testify about him that everyone who believes in him receives forgiveness of sins through his name.” Acts 10:43
In him we have redemption through his blood, the forgiveness of sins, in accordance with the riches of God’s grace Ephesians 1:7
he saved us, not because of righteous things we had done, but because of his mercy. He saved us through the washing of rebirth and renewal by the Holy Spirit, whom he poured out on us generously through Jesus Christ our Savior Titus 3:5-6
For this reason Christ is the mediator of a new covenant, that those who are called may receive the promised eternal inheritance—now that he has died as a ransom to set them free from the sins committed under the first covenant. Hebrews 9:15
Therefore, my brothers, I want you to know that through Jesus the forgiveness of sins is proclaimed to you (Acts 13:38) to give his people the knowledge of salvation through the forgiveness of their sins (Luke 1:77). Jesus will only forgive our sins under one baptism like John the baptist said baptize you with water, but he will baptize you with the Holy Spirit (Mark 1:8). I baptize you with water for repentance. But after me will come one who is more powerful than I, whose sandals I am not fit to carry. He will baptize you with the Holy Spirit and with fire (Matthew 3:11). No other baptism is as powerful as Jesus’ baptism to forgive our sins. We just need to ask Jesus to baptise thus forgiving our sin through the proclamation of His Name because everyone who calls on the name of the Lord will be saved (Acts 2:21).