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.
They could look at your phone or computer and see which Facebook account you are logged into. This won't prove you created it but even logging into it is possibly a ToS violation.