Here is the Didache on baptism, from the first century:
http://www.spurgeon.org/~phil/didache.htm
http://reluctant-messenger.com/didache.htm
In point of fact, however, we do not read of "baptism in the name of Jesus" in Acts. Instead, we read of baptism "in the name of Jesus Christ" (2:38, 10:48), and "in the name of the Lord Jesus" (8:16, 19:5). So even Acts is not united in its expression.
In reality, neither of the expression Acts uses is a baptismal formula. Instead, they are designations of the kind of baptism and are intended to distinguish it from the multiple other kinds of baptism which were at that time present in first century Mediterranean culture.
Thus the four references in Acts -- which use two different expressions -- do not overrule Jesus' explicit command to baptize "in the name of the Father and of the Son and of the Holy Spirit" (Matthew 28:19). This is an explicit, formal command concerning the propagation of the sacrament, whereas Acts's references are merely incidental, casual references to the fact that it was performed, as indicated by the two different expressions that are used in them. It is thus Christ's explicit, formal command which takes precedence over the other, diverse ones.
EARLY CHURCH ON BAPTISM:
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 [A.D. 70]).
Tatian the Syrian
"Then said Jesus unto them, I have been given all authority in heaven and earth; and as my Father has sent me, so I also send you. Go now into all the world, and preach my gospel in all the creation; and teach all the peoples, and baptize them in the name of the Father and the Son and the Holy Spirit; and teach them to keep all whatsoever I commanded you: and lo, I am with you all the days, unto the end of the world [Matt. 28:18-20]" (The Diatesseron 55 [A.D. 170]).
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 [A.D. 215]).
Tertullian
"After his resurrection he promises in a pledge to his disciples that he will send them the promise of his Father; and lastly, he commands them to baptize into the Father and the Son and the Holy Ghost, not into a unipersonal God. And indeed it is not once only, but three times, that we are immersed into the three persons, at each several mention of their names" (Against Praxeas 26 [A.D. 216]).
Origen
"Why, when the Lord himself told his disciples that they should baptize all peoples in the name of the Father and of the Son and of the Holy Spirit, does this apostle [Paul] employ the name of Christ alone in baptism, saying, We who have been baptized into Christ; for indeed, legitimate baptism is had only in the name of the Trinity" (Commentary on Romans 5:8 [A.D. 248]).
The Acts of Xantippe and Polyxena
"Then Probus . . . leapt into the water, saying, Jesus Christ, Son of God, and everlasting God, let all my sins be taken away by this water. And Paul said, We baptize thee in the name of the Father and Son and Holy Ghost. After this he made him to receive the Eucharist of Christ" (Acts of Xantippe and Polyxena 21 [A.D. 250]).
Cyprian of Carthage
"He [Jesus] commanded them to baptize the Gentiles in the name of the Father and of the Son and of the Holy Spirit. How then do some say that though a Gentile be baptized . . . never mind how or of whom, so long as it be done in the name of Jesus Christ, the remission of sins can followwhen Christ himself commands the nations to be baptized in the full and united Trinity?" (Letters 73:18 [A.D. 253]).
http://reformationtoday.tripod.com/chemnitz/id44.html