Romans 6: 3-4 (NASB): Or do you not know that all of us who have been baptized into Christ Jesus have been baptized into His death? Therefore we have been buried with Him through baptism into death, in order that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life.
Baptism is so misunderstood. The Greek word means "immersion or burial". It is a symbolic gesture to show God we believe and will obey. We are buried in water as Jesus was buried, and we rise to a different life as He arose. Even Jesus was baptized. This was not for the remission of sins as the Apostle Peter instructs us in Acts 2:38. Is didn't save Jesus as Peter tells us baptism now saves us in I Peter 3:21. Jesus was baptized, immersed in the water of the Jordan River, as He put it in Matthew 3:15: "to fulfill all righteousness".
If you study the Bible without bias, you will see that everyone in the history of the early church, the Book of Acts, was baptized. Peter commanded in in Acts 2, and again when he first took the gospel to Gentiles in Acts 10. Paul, in Acts 19, found about twelve men in Ephesus who had been baptized under John's teaching. He explained to them about Christ and they were then baptized in the name of the Lord Jesus.
"In the name of" means doing something by the authority of the entity being referenced. "In the name of the law" means by the authority granted by the government. To "obey the gospel" is to obey Jesus and the Apostles by submitting to baptism in the name of the Lord Jesus, and Jesus Himself instructs in Matthew 28:19-20.