Jesus said to baptize in the "name," not to use a phrase. The other info you provided came from outside of the inspired word of God.The phrase in the name of the Father, and of the Son, and of the Holy Spirit was instituted by Jesus.
It was used before 325AD as I have already shown, first in a quote from a 1st century document, then in a 2nd century document.
Do you want more?
As provided previously the word states that in Jesus dwells all the fullness of the Godhead (Father, Son and Holy Ghost) bodily. (Col 2:9) After that statement in verse 9 of Colossions, the scripture goes on to speak of water baptism in verse 12:
"For in him dwelleth all the fulness of the Godhead bodily.
10 And ye are complete in him, which is the head of all principality and power:
11 In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ:
12 Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead. Col 2:10-12