A little history first, this is from the Didache, a very early church manual,
CHAPTER 7
Baptism
1 Concerning baptism, baptise thus: Having first rehearsed all these things, “baptise, in the Name of the Father and of the Son and of the Holy Spirit,” in running water; 2 but if thou hast no running water, baptise in other water, and if thou canst not in cold, then in warm. 3 But if thou hast neither, pour water three times on the head “in the Name of the Father, Son and Holy Spirit.” 4 And before the baptism let the baptiser and him who is to be baptised fast, and any others who are able. And thou shalt bid him who is to be baptised to fast one or two days before.
earlychristianwritings.com/text/didache-lake.html
Those who baptise in Jesus name only, belong to a system known as modalism or sabellism. They deny the doctrine of the Trinity outright. They believe that there is only one person in the godhead and that is Jesus. They use Acts 2:38 as their proof text for their mode of baptism, and ignore the clear directions given by Jesus himself in Matthew 28, and ignore the clear history given in the Didache.
Read Acts 2 for context, in this section of scripture the authority of Jesus is being emphasized. So, the person above who said, that it simply has to do with the authority of the teachers, Jesus is correct.
32God has raised this Jesus to life, and we are all witnesses of the fact. 33
Exalted to the right hand of God, he has received from the Father the promised Holy Spirit and has poured out what you now see and hear. 34For David did not ascend to heaven, and yet he said,
" 'The Lord said to my Lord:
“Sit at my right hand
35until I make your enemies
a footstool for your feet.” ’
36"Therefore let all Israel be assured of this: **God has made this Jesus, whom you crucified, both Lord and Christ." **
37When the people heard this, they were cut to the heart and said to Peter and the other apostles, “Brothers, what shall we do?”
38Peter replied,
"Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit. 39The promise is for you and your children and for all who are far off—for all whom the Lord our God will call."
40With many other words he warned them; and he pleaded with them, “Save yourselves from this corrupt generation.” 41Those who accepted his message were baptized, and about three thousand were added to their number that day.
42They devoted themselves to the apostles’ teaching and to the fellowship, to the breaking of bread and to prayer. 43Everyone was filled with awe, and many wonders and miraculous signs were done by the apostles. 44All the believers were together and had everything in common. 45Selling their possessions and goods, they gave to anyone as he had need. 46Every day they continued to meet together in the temple courts. They broke bread in their homes and ate together with glad and sincere hearts, 47praising God and enjoying the favor of all the people. And the Lord added to their number daily those who were being saved.