In Jewish thought, I should know since I studied in Temple that "in the name of" refers to authority. I already posted a link to that effect. Luke also, used a well know shorthand in Acts 2:38.
7 Now about baptism: this is how to baptize. Give public instruction on all these points, and then "baptize" in running water,
"in the name of the Father and of the Son and of the Holy Spirit."498 2If you do not have running water, baptize in some other. 3If you cannot in cold, then in warm. If you have neither, then pour water on the head three times "
in the name of the Father, Son, and Holy Spirit."
499 4Before the baptism, moreover, the one who baptizes and the one being baptized must fast, and any others who can. And you must tell the one being baptized to fast for one or two days beforehand.
5You must not let anyone eat or drink of your Eucharist except those
baptized in the Lord's name.
Acts 2:38
Peter said to them, “Change your hearts and lives and be baptized, each one of you, in the name of Jesus Christ.
Acts 8:12
But Philip told the people the Good News about God’s kingdom and the power of Jesus Christ. Men and women believed Philip and were baptized.
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Acts 8:13
Simon himself also believed, and after he was baptized, he stayed close to Philip. When he saw the miraculous signs and powerful things Philip did, he was amazed.
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Acts 8:16
These people had been baptized in the name of the Lord Jesus, but the Holy Spirit had not yet come down on any of them. This is why Peter and John prayed.
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Acts 8:36
While they were traveling down the road, they came to some water. The official said, “Look, here is water! What is stopping me from being baptized?”
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Acts 8:38
Then the official ordered the chariot to stop. Both Philip and the official went down into the water, and Philip baptized him.
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Acts 9:18
Immediately, something that looked like fish scales fell off Saul’s eyes. He was able to see! Then he got up and was baptized.
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Acts 10:37
“You know what has happened all over Judea. It began in Galilee after John told the people they needed to be baptized.
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Acts 10:47
“How can anyone object to these people being baptized in water? They have received the Holy Spirit the same as we did!”
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Acts 10:48
So Peter told them to baptize Cornelius and his relatives and friends in the name of Jesus Christ. Then they asked Peter to stay with them for a few days.
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Acts 11:16
Then I remembered the words of the Lord Jesus: ‘John baptized people in water, but you will be baptized in the Holy Spirit.’
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Acts 13:24
Before he came, John told all the people of Israel what they should do. He told them to be baptized to show they wanted to change their lives.
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Acts 16:15
She and all the people living in her house were baptized. Then she invited us into her home. She said, “If you think
I am a true believer in the Lord Jesus, come stay in my house.” She persuaded us to stay with her.
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Acts 16:33
It was late at night, but the jailer took Paul and Silas and washed their wounds. Then the jailer and all his people were baptized.
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Acts 18:8
Crispus was the leader of that synagogue. He and all the people living in his house
believed in the Lord Jesus. Many other people in Corinth also listened to Paul. They, too, believed and were baptized.
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Acts 18:25
He had been taught about the Lord and was always excited to talk to people about Jesus. What he taught was right, but the only baptism he knew about was the baptism that John taught.
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Acts 19:3
Paul asked them, “So what kind of baptism did you have?” They said, “It was the baptism that John taught.”
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Acts 19:4
Paul said, “John told people to be baptized to show they wanted to change their lives. He told people to believe in the one who would come after him, and that one is Jesus.”
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Acts 19:5
When these followers heard this, they
were baptized in the name of the Lord Jesus.
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Acts 22:16
Now, don’t wait any longer. Get up, be baptized and wash away your sins, trusting in Jesus to save you.’
Baptized in the name of ??? is just shorthand by Luke for the Father, Son and Holy Spirit