Anonymity is not the same thing as privacy. You do not get to be anonymous by any government standard. Because being anonymous means you get to dodge responsibility when you do something wrong. Privacy is the right not to divulge anything about yourself that you wish not to divulge.
No legitimate Casino in this world is going to help you be anonymous. They have regulators breathing down their necks and looking at their hands at all times. Casinos have a duty to weed out bad actors like money launderers, scammers, terrorists and so on.
Just because the KYC is not demanded when you register an account does not mean you will not have to give your KYC on demand, later.
In fact, every legit casino which does not demand KYC on registration mentions this in their Terms Of Service.
Do not forget that KYC is a way to prevent fraud. No person who has passed KYC will cheat. Another thing is that the casino must provide such conditions that it is impossible to purchase other people's accounts with KYC or pass fake KYC. If casino conducts KYC, then everything should be as honest as possible.