If this is the case, do you think claiming at least our character names could be beneficial to Town overall? Or expose townies too much despite not revealing our abilities?
I think the host might have provided Mafia with fake town names or even sheets, so maybe not a consistent idea.
But I think that fake town names/sheet would be more likely to be less relevant characters in the arc story, so maybe one would be capable of distinguishing a fake claim from a non-fake, albeit that is not a granted.