Earlier quoted context omitted.
I can also be anonymous if I never speak or leave my house, but that's not really how it works, is it?
No, you can't. Your house has to be registered to someone and you have to declare who lives in it, if it's yours. Anonymity is not about being a private person.
I don't think this is true in every jurisdiction. You can certainly have a property registered under a corporate entity, and there are jurisdictions in the US that allow for anonymous corporate ownership. Further, I'm not aware of any requirement where you must declare who is residing in a property. I've had family members from abroad reside in my house for over a year without informing any authorities, for example.