The importance of the command for the disciples no longer to speak or to teach in the name of Jesus is that it now gives the legal basis for the further persecution recorded in the next chapter.
The contents of verse 18 are a conclusion to what has been recommended in verse 17 (hence the transitional particle so) and a transition to the following paragraph.
Inasmuch as the pronoun them in this context refers specifically to Peter and John, it is perhaps necessary to specify these individuals. Otherwise some may understand this to include the man who was healed. From the standpoint of the discourse structure, this is a somewhat awkward situation in that the lame man has been dropped from the episode without specific mention of what happened to him.
Many languages require the substance of what was told to Peter and John to be expressed in direct discourse, for example, “told them, In no way are you to speak or teach using the name of Jesus.”
Though the term name certainly figures prominently in this type of context, it may be necessary in some instances to translate as “you must under no circumstances speak or teach about Jesus.”
Quoted with permission from Newman, Barclay M. and Nida, Eugene A. A Handbook on The Acts of the Apostles. (UBS Handbook Series). New York: UBS, 1972. For this and other handbooks for translators see here .
