70% of crypto exchanges allow trading and withdrawal without any verifications, you just have to do research on them is all, here are few ones I used with no KYC needed ..
Even if you don't complete KYC on those exchanges, you still need to transfer fiat money to them via a bank account, a credit card, PayPal, or some other electronic method, all of which come attached with the minimum of your name and phone number, but potentially also your address, account number, etc., and so are in no way anonymous. Furthermore, pretty much all centralized exchanges track your bitcoin deposits and withdrawals to report to various governments and third parties, and all centralized exchanges can freeze or lock your account at any time and demand that you complete KYC, holding your coins hostage unless you do.
Any centralized exchange is an incredibly poor choice if you are interested in maintaining privacy, and it is utterly impossible to be anonymous when using them.