Translation:Identify each other!
The prefix pe- shows that the command is being given to multiple people. The suffix -chuq indicates that whatever the action is, they will do it to each other. In this case the action they are doing is "identify". The person making the demand obviously does not recognize their identities and is asking each one to identify the other, rather then each identifying themselves. It does seem to be an odd request. Maybe he has reason to believe they are using false identities and he hopes by asking each one to identify the other he can trip them up because they will not have memorized the details of the other as well as their own.
Imagine if the questioner is talking to Torg and Mara.
Then pengu''egh! (Identify yourselves!) would be like saying to Torg, "Identify yourself!" and to Mara, "Identify yourself!". He would expect Torg to say torgh jIH (I am Torg) and Mara to say mara jIH.
On the other hand, pengu'chug! (Identify each other!) would be like saying to Torg, "Identify the other person!" and to Mara, "Identify the other person!". He would expect Torg to say mara ghaH or mara ghaH ghotvetlh'e' (She is Mara; That person is Mara) and Mara to say torgh ghaH (ghotvetlh'e').