I personally believe that the double-crosser Sirius heard the other DEs discussing was Snape - not Peter - Sirius never hears them mention Peter's name.
They definitely didn't mention Severus by name, because Sirius didn't know he was a DE. But if they did mention Peter by either name or nickname they could have learned it from Sirius. Before he managed to transform and receive some reprieve from the influence of dementors he must have spent much time dwelling on Peter and his perfidy.
They definitely didn't mention Severus by name, because Sirius didn't know he was a DE. But if they did mention Peter by either name or nickname they could have learned it from Sirius. Before he managed to transform and receive some reprieve from the influence of dementors he must have spent much time dwelling on Peter and his perfidy.