but how would they find this "name of your facebook account"?
yes they will have my ID, real name, finger prints, etc.
but how would they figure out that I am using facebook account "puppy123"? And even if they would suspect it somehow (someone would report it), I can simply deny and there is no evidence that I am in fact owner of that account.
or what am i missing?
If you're logged into it on your phone/computer, it's evidence that you created the account. Or else you logged into someone else's account which is also a ToS violation.