Hi @gina_dimaio
Welcome to the Canvas Community, and it's good to see that you're generally enjoying the Canvas feature set. And the fact that you have already tackled peer assignments successfully is great!
Unfortunately, there is no real clear-cut way to hide group membership from students outside of the group other than hiding the People menu altogether via the Navigation menu in Settings. This would be true, frankly, even if the groups were not self signup, since even for faculty-assigned groups a student can still go into People and view other groups' memberships if they were so inclined.
Even with disabling People, there might be some other sneaky ways students could ascertain group memberships, but I can't think of any at the moment. (And they definitely can always see members for their own groups; though I realize that's not what you're asking.)
Unfortunately, I fear you will have to chalk this up to a lesson learned when having students submit assignments that will be peer reviewed anonymously. Be sure they never display their name on the submission, nor (as you have found) their group membership. But for now, at least, hiding the People menu should suffice. But if you plan on having more self signup groups in the future, you will definitely want to re enable it later on!
I hope this helps a bit, Gina!
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