so i run a server that uses hamachi. so sadly anyone can take a name and therefore also be mod/admin. so what i suggest is that when you enter the server you have no permissions at all, and you get a window or text saying that you need to enter a password to unlock that account. if you succeed with the password then you get permissions set for that account. if you however fail with the password after 3 times you'll get kicked. anyone want to take this on?
Even using hamachi, I think it should still authenticate accounts. Are you running the server in offline mode? Why not just switch it to online?