I suppose there are privacy settings in facebook which you can block anonymous from sending you message, or even hide your profile from the public.
The whole fucking idea of facebook to cheat people sharing their information for free, e.g. family, friends, relationship, education background, hobbies, etc. You guys must have underestimated how valuable these information is, especially when such information is gathered at the global level.
Fuck facebook. I have an account with a fake name and a blank profile.