If you want privacy and anonymity, you can use decentralized exchange like Bisq.
But if you are a trader, you may have no option than to use central exchanges. We traders can only prefer to use no-KYC exchange but this is shrinking as more centralized exchanges that are no-KYC starts to ask for KYC. We do not have that privacy, but we should not leave our coins on exchanges, that is very important. All coins should be stored on noncustodial wallet.
kycnot.me list Kucoin, but with low trust score if 4 because it is a centralized exchange. It is the first no-KYC exchange that we recognized, but no more because they will start mandating KYC starting from July 15th, which is just notkre than two weeks from now.
If you say no CEX at all, that is not possible, traders rely on CEX to trade. If you want privacy, do not trade and focus only on buying and selling bitcoin using decentralized exchanges like Bisq or the use of this forum.