Most Helpful Girl
No, only the admins can.
Editors - Are those who write very well written mytakes.
When you gain this status your mytakes and automatically promoted (instead of having to wait for it to be promoted by admins).
Moderators - There are different levels (Super, Uber and Regular moderator). We cannot see who anonymous users are.
Only the Admin can.
But they have the ability to see who is who for professional purposes (not invading ones privacy), but reducing the trolls in this community.1