In John 4:1-3, in whose name were Jesus' disciples' baptizing?

The Passage which comes directly after John 3:16 explaining the need of water baptism, explains that John's role deminishes as Christ's increases.

John 3:23-36 After these things came Jesus and his disciples into the land of Judaea; and there he tarried with them, and baptized. And John also was baptizing in Aenon near to Salim, because there was much water there:and they came, and were baptized. For John was not yet cast into prison. Then there arose a question between some of John's disciples and the Jews about purifying. And they came unto John, and said unto him, Rabbi, he that was with thee beyond Jordan, to whom thou barest witness, behold, the same baptizeth, and all men come to him. John answered and said, A man can receive nothing, except it be given him from heaven. Ye yourselves bear me witness, that I said, I am not the Christ, but that I am sent before him. He that hath the bride is the bridegroom:but the friend of the bridegroom, which standeth and heareth him, rejoiceth greatly because of the bridegroom's voice:this my joy therefore is fulfilled. He must increase, but I must decrease. He that cometh from above is above all:he that is of the earth is earthly, and speaketh of the earth:he that cometh from heaven is above all. And what he hath seen and heard, that he testifieth; and no man receiveth his testimony. He that hath received his testimony hath set to his seal that God is true. For he whom God hath sent speaketh the words of God:for God giveth not the Spirit by measure unto him. The Father loveth the Son, and hath given all things into his hand. He that believeth on the Son hath everlasting life:and he that believeth not the Son shall not see life; but the wrath of God abideth on him.

The order of the passage is Christ proclaiming the neccesity of Water Baptism,

john 3:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life

Then a Demonstration of his statement

john 3:23 After these things came Jesus and his disciples into the land of Judaea; and there he tarried with them, and baptized.

The question of weather Johns baptism remains valid in the quote above answered.

He must increase and I must decrease.

Then all the apostles ran around asking "Have you accepted Jesus as your personel Lord and Savior"

John 3???

and "If you died right now, would you know for certain that you have been saved"

John ?????

The baptism of repentance was continued by His disciples in the Lords earthly ministry. Those who were Baptized came to hear the Good news and heard it, but the Holy Spirit was not yet given in order that the Apostles could baptism into Christs death. Jesus's earthly ministry represented a transitional period in Gods Saving Plan. To be baptized in the Name of the Father Son and Holy Spirit is to be baptized into Christ's Death, and raised to new life. This reality would be impossible to achieve during Christ's ministry as he had not suffered his passion. However, the validity of a Baptism for those, and transfering the gift of the Holy Spirit is not subject to time and space as we are. All things are possible for God. There are mysteries known only to God and this is understood by his Church.

There are also more than one way to be Baptized. 1st By Water, 2nd By Martyrdom, and third by Mystery.

I hope that helps

It was John's baptism because the second baptism (by fire or by the holy ghost) didn't come until Jesus was resurrected.

See John 7:39 (But this spake he of the Spirit, which they that believe on him should receive: for the Holy Ghost was not yet given; because that Jesus was not yet glorified.)

There's no indication of either.

It happened that while Apollos was at Corinth, Paul passed through
the upper country and came to Ephesus, and found some disciples. He
said to them, "Did you receive the Holy Spirit when you believed?"
And they said to him, "No, we have not even heard whether there is a
Holy Spirit." And he said, "Into what then were you baptized?" And
they said, "Into John's baptism." Paul said, "John baptized with the
baptism of repentance, telling the people to believe in Him who was
coming after him, that is, in Jesus." When they heard this, they were
baptized in the name of the Lord Jesus. And when Paul had laid his
hands upon them, the Holy Spirit came on them, and they began
speaking with tongues and prophesying. (Act 19:1-6)

• In Acts 19:1-6, there's no indication anyone had to be baptized again, other than John's disciples who still didn't realize Jesus was the Messiah.
• In John 4, Jesus' disciples were already following Jesus, instead of John. There's no indication Jesus' disciples were baptizing in any name other than Jesus'.

The command to baptize in the name of the Father, Son and Holy Ghost was given only at the ascension of Jesus.

Before the ascension, there is no indication that there was a name used at all. John just said,"Repent and be baptised for the time is at hand".

So John did not baptize using any name. John's baptism is called "baptism of repentance" in Acts 19.

So until Jesus gave the express command during ascension, no name was used during baptism.