Is it really important how a person is baptized?

Yes, water baptism by immersion in the name of JESUS for the remission of sins is very important. 

It is by baptism in Jesus name that our sins are remitted/washed away/buried, because by the name of Jesus the blood of Jesus is applied to a person. (Matthew 26:28, Acts 2:38, Acts 10:43, 48, Acts 22:16, Revelation 1:5, Exodus 12:5-7, 13, 1Peter 1:18-19, Revelation 12:11, Romans 6:3-4, Colossians 1:14, Colossians 2:11-12. 1Corinthians 6:11.) 

Water baptism in Jesus name is a blood covenant. It is compared to circumcision, which is also a blood covenant. In circumcision, the flesh is cut off, the person is given their name, blood is shed, and the person is joined to God’s people. (Genesis 17:14, Colossians 2:11-12, Luke 2:21.) Water baptism in Jesus name is the New Covenant fulfillment of circumcision in the Old Covenant. In baptism in Jesus name, it represents Jesus’ cutting off of His flesh by death, and His blood was shed. It represents our cutting off the lusts of our flesh and sin by repentance and baptism, and applying Jesus death and blood to us personally. We are given the name of Jesus in water baptism in Jesus name, just as in circumcision the name is given. The name of Jesus is called upon us. (Acts 22:16, Acts 15:17, Acts 9:21, James 2:7.)

Water baptism is one of the two ingredients of the New Birth of John 3:3-5 which Jesus said is necessary to enter the kingdom of God. Our spiritual life lines up with the natural, from conception to adulthood. Just as there is a mother and father involved with natural birth, there is a mother and Father involved with our spiritual birth. Only the mother – the church – can water baptize a person in Jesus name. Only the Father – Jesus – can Spirit baptize a person with His Holy Spirit (Holy Ghost). It takes mother and Father and they cannot be interchanged in their roles. Jesus gave authority to the church to remit sins in His Great Commission found in the gospel of John 20:21-23, and this authority was used on the Day of Pentecost when the church first began. (Acts 2:38-41.) The church is responsible for baptizing souls in Jesus name. On the other hand, only Jesus can fill a person with His Spirit. No man can do this. When a person is filled with the Spirit of Jesus, the person speaks in other tongues as the Spirit gives the utterance. (Acts 2:4, Acts 19:6, Acts 10:45-46.) Just as when a baby is born from its mother, there is water that comes forth, then the baby takes its first breath of air and lets out a cry, letting everyone know he has taken his first breath. (The sound of the infilling of the Spirit is spoken of by Jesus when He is speaking of being born of the Spirit. Jesus compares the Holy Spirit with the wind. He said the wind blows where it lists and you hear the SOUND but can’t tell where it came from and where it is going – so is every one that is born of the Spirit. (John 3:8.) When a person is born of the Spirit, they too let out a sound. What is heard is the sound of the Spirit that has just filled them. It is speaking in tongues as the Spirit gives the utterance.) Both births, water and the Spirit, are necessary to enter the kingdom of God. (John 3:5.)

The Bible says we are saved by baptism. (1Peter 3:21.) Water baptism in Jesus name is compared to Noah and the flood. The sin of the world in Noah’s day was washed away, while Noah was saved by the water, safe in the ark. Our sins are washed away, while we are saved by water baptism in Jesus name. The ark is a type of the church. (i.e. One door – Jesus is the door.) We enter into the church by water and Spirit baptism.

Water baptism in Jesus name is an essential part of obedience to the gospel. The gospel is the death, burial, and resurrection of Jesus. (1Corinthians 15:1-4, Romans 6:1-23.) We must obey the gospel in order to be saved. (2Thessalonians 1:8, 1Peter 4:17, Romans 10:16.) Obeying the gospel is by repentance and water baptism in Jesus name, and receiving the gift of the Holy Ghost, which follows Jesus’ death (crucifixion), burial, and resurrection. (Romans 6:1-4, Colossians 2:11-12, Matthew 16:24, Mark 8:34, Luke 9:23, Acts 2:38.)