In John 4:1-3, in whose name were Jesus' disciples' baptizing? In regards to John 4:1-3, were Jesus' disciples in this passage baptizing with John's baptism?  If not, and they were baptizing in the name of Jesus, did the people who receive this baptism have to be re-baptized to receive the Holy Spirit (as did those who received John's baptism)?
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'.