Does it matter what "formula" is used during a baptism?
The instruction in the commission given to the apostles is very specific:
Matthew 28:19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit:
From this, the correct form of words to be used at a baptism into Jesus Christ for the remission of past sins is – “You are baptised in the name of the Father, and of the Son and of the Holy Spirit”
Although there are other references which speak of being baptised in the name of Jesus, there seems little reason to doubt that the form of words commanded would be used.
Acts 2:38 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 Spirit.
Acts 8:16 (For as yet he was fallen upon none of them: only they were baptized in the name of the Lord Jesus.)
Acts 10:48 And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.
Acts 19:5 When they heard this, they were baptized in the name of the Lord Jesus.
I can think of no reason why the name of the Father and the Holy Spirit would be omitted when it is specifically commanded.
Those who come to Jesus Christ are drawn by the Father and sanctified by the Spirit of God through the word preached by Christ.
John 6:44 No man can come to me, except the Father which hath sent me draw him…
Romans 15:16 That I should be the minister of Jesus Christ to the Gentiles, ministering the gospel of God, that the offering up of the Gentiles might be acceptable, being sanctified by the Holy Spirit.
John 6:63 It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, they are spirit, and they are life.
John 15:3 Now ye are clean through the word which I have spoken unto you.
I hope you find this helpful.