As someone with elevated permissions, I presumed that I saw who reported the abuse because of my permissions, but does the author also know who reported the abuse? I assumed that it was anonymous, but I just got a note from someone asking why I reported abuse on a particular post.
I believe that anyone who has moderation (and/or admin?) permissions for the location will also see the abuse report. We don't use moderation, so I'm a little fuzzy on the process.