When we are baptized in Jesus name, God's holy, saving name, “JESUS” becomes our name. The name “Jesus” is called upon us. (Acts 4:12).

The name “Jesus” is NOT called upon us if we were baptized with, “I baptize you in the name of the Father, and of the Son, and of the Holy Ghost.” This baptism is using titles, not the NAME, which is JESUS. All baptisms in the Bible were in the name of JESUS, not in a trinity formula, which was adopted later by the Catholic church around 325 AD.

"And when they were come to Jerusalem, they were received of the church, and of the apostles and elders, and they declared all things that God had done with them." - Acts 15:4 KJV

"And after they had held their peace, James answered, saying, Men and brethren, hearken unto me: Simeon [Peter] hath declared how God at the first did visit the Gentiles, to take out of them a people for his name. And to this agree the words of the prophets; as it is written, After this I will return, and will build again the tabernacle of David, which is fallen down; and I will build again the ruins thereof, and I will set it up: that the residue of men might seek after the Lord, and all the Gentiles, upon whom my name is called, saith the Lord, who doeth all these things." - Acts 15:13-17 KJV

It is recorded in Acts 10 “how God at the first did visit the Gentiles, to take out of them a people for His name.” The name of Jesus was called upon the Gentiles when Peter water baptized them in Jesus name in Acts 10:48.

("And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. For they heard them speak with tongues, and magnify God. Then answered Peter, Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we? And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days." - Acts 10:45-48 KJV)

By baptism in Jesus name, we are given the name of Jesus.

"Do not they blaspheme that worthy name by the which ye are called?" - James 2:7 KJV

"Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost." - Acts 2:38 KJV

"And now why tarriest thou? arise, and be baptized, and wash away thy sins, calling on the name of the Lord." - Acts 22:16 KJV