I prefer to use original document both on gambling site (sportsbook as well as casino) as well as crypto exchange site. Casue if I use any fake info that might be used by someone else too. If that happens then the account of mine can be locked due to the use of fake document. And I not only use the real document but also I suggest everyone to use real document.
This is the right approach obviously since it's quite easy to get screwed if you provide fake documents by gambling sites(FIAT and Crypto), but I can also understand why many gamblers choose to submit fake documents.
They do this because they are aware of all the information leaking incidents which happen on a regular basis which is why they prefer gambling anonymously.