If we were to find an explicit formulat it would be "in the name of the Father, Son and Holy Spirit" (matt 28:19)
But then we find the apostles disobeying the command of Christ and making some false converts by baptising in the name of Jesus only in Acts 19:5.
Just kidding.
There is strong evidence from many early church writings that the early church baptised in the name of the Father, Son and Holy Spirit.
The Didache which is really an early church pastoral manual:
70 AD The Didache "After the foregoing instructions, baptize in the name of the Father, and of the Son, and of the Holy Spirit, in living [running] water. If you have no living water, then baptize in other water, and if you are not able in cold, then in warm. If you have neither, pour water three times on the head, in the name of the Father, and of the Son, and of the Holy Spirit. Before baptism, let the one baptizing and the one to be baptized fast, as also any others who are able. Command the one who is to be baptized to fast beforehand for one or two days" (Didache 7:1).
215 AD Hippolytus "When the one being baptized goes down into the water, the one baptizing him shall put his hand on him and speak thus: `Do you believe in God, the Father Almighty?' And he that is being baptized shall say: `I believe.' Then, having his hand imposed upon the head of the one to be baptized, he shall baptize him once. Then he shall say: `Do you believe in Christ Jesus . . . ?' And when he says: `I believe,' he is baptized again. Again shall he say: `Do you believe in the Holy Spirit and the holy Church and the resurrection of the flesh?' The one being baptized then says: `I believe.' And so he is baptized a third time" (The Apostolic Tradition 21).
So from this, flowing water, or natural water systems, rivers streams etc are preferable.
And yes, pouring on the head is acceptable as a last resort.
Fasting - well does anyone do that anymore?
So those people who say you MUST be baptised by full immersion - think again. You probably aren't baptising properly according to the early church practices anyway if the converts don't fast one or two days beforehand, or if you aren't using living water (eg rivers, streams etc).
Those people who say you MUST be baptised in the name of Jesus only - think again. Again, you probably already not doing it properly if the converts don't fast beforehand, or aren't baptised in a river or something like that.
If anything, it seems important to the early church that the person is baptised in the name of the Father, Son and Holy Spirit, not just the name of Jesus. No point baptising someone if they don't believe in the Father and/or the Spirit.