Immediately before Jesus ascended into heaven after His resurrection, He sent His disciples out with this command: "Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost" (Matthew 28:19). From this command we take the baptismal formula whereby converts are baptized in the name of the Father, the Son, and the Holy Ghost. This is the method taught by Jesus Christ Himself.
I am not an expert on the doctrine of the Apostolic Church, but I know that they pervert the biblical teaching of the trinity. As I understand it, they teach that God operates in different times as the Father, the Son, and the Holy Ghost. Therefore, Jesus is the the name of all three persons of the trinity. In this short answer, I cannot even begin to tell you the full danger of this doctrine. But it is full of heresy. Also, because Acts 2:38, Acts 8:16 and Acts 19:5 refer to being baptized in the name of Jesus Christ or the Lord Jesus, they claim that this is the required and necessary formula today.
To do something "in the name of" someone else means to do it by their authority. It can also refer to doing something in the place of another. It does not only refer to words spoken at the time something is done. We are baptized by the authority of (in the name of) Jesus. He commanded it and we can baptized because He died on the cross for our sins and made salvation through His blood possible. Without the salvation that comes by trusting in the death, burial, and resurrection of Christ, we have no right or authority to be baptized. Baptism also identifies us with Jesus Christ. The placing of the body under water is a picture of the death and burial of Christ. The coming up out of the water is a picture of resurrection. In both of these meanings we are baptized in the name of Jesus Christ today.
However, this does not mean that the formula we use--which is taken from the very words of Christ--is invalid. Jesus is the name given to the Son in his humanity. Jesus was filled with the Holy Ghost and indwelled by the Father, but He was not the Holy Ghost or the Father. Please beware of the teachings of the Apostolic Church. They are very wrong.
