Here is a reply from someone else who was in a simular discussion elsewhere:
I believe they did speak the name of Jesus at some point during the baptism, not the English version of course, but whichever language was contemporary (Jesus is smart enough to know we are speaking to Him whether we are using Greek, Russian, Spanish, etc.) It may not have been exactly like we do it today when we dunk them in the water and say "[name of person], I baptize you in the Name of Jesus Christ...", but at some point they needed to tell the person that they are getting baptized in the name of Jesus. Below this paragraph are three verses where the name of Jesus was invoked by spoken words. The verses are not related to baptisms, but they show that yes, indeed, speaking His name was practiced.
"Then Peter said, 'Silver and gold have I none; but such as I have give I thee: In the name of Jesus Christ of Nazareth rise up and walk.'"
Acts 3:16
"...But Paul, being grieved, turned and said to the spirit, 'I command thee in the name of Jesus Christ to come out of her.' And he came out the same hour."
"Then certain of the vagabond Jews, exorcists, took upon them to call over them which had evil spirits the name of the LORD Jesus, saying, 'We adjure you by Jesus whom Paul preacheth.."
Acts 19:13
If one were not baptized with some kind of spoken reference, how would one know who he or she was baptized "in"? The baptizer could be doing it "in the name" of The Great Pumpkin for all we know. There was a similar situation in the Bible where people were apparently prone to identify baptism "into" someone other than Jesus, which Paul condemed: "Is Christ divided? was Paul crucified for you? or were ye baptized in the name of Paul? I thank God that I baptized none of you, but Crispus and Gaius; Lest any should say that I had baptized in mine own name." (
1 Corinthians 1:13-15). So, it's extremely important that the one being baptized is made aware of exactly who they are being baptised into, and who they are NOT being baptised into, and the only way to do that is to speak it plainly and clearly.
Paul asked a group in
Acts 19 about their own baptism methods, and then re-baptized them, so again we know it was important to the original church to know precisely who we were baptized into.
What we actually speak aloud is powerful; for example, "blasphemy" is defined as the audible spoken word against God. Jesus said blasphemy against the Holy Spirit is the only unforgivable sin. Apparently just "thinking it" wasn't unforgivable, but speaking that "thinking" aloud is.