If you have a false facebook account, you broke facebooks ToS! That means you accessed facebooks servers without authentication!! That is a crime under e.g. the CFAA!!!
You'd have had to lie to Customs and Border Protection, which is already probably a crime and quite likely sufficient to get you detained and deported.
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.
