There were a variety of baptisms extant at that time, such as the baptisms of pagan cults like Mithraism, John the Baptist's baptism, or Jewish proselyte baptism. So when the phrase "baptize in the name of Jesus" is used, it is simply a synecdoche for "Christian baptism." In other words, these passages are not setting forth the formula but distinguishing "Christian" baptism from others.
When the command to baptize is given in Matt 28:19, they are told to do so "in the name of the Father and of the Son and of the Holy Spirit." This is also known in a shorter label as baptized "in the name of Jesus" in Acts.
See this Catholic Answers tract also.