You can't really expect privacy if you are using centralized exchanges. Most of them require that you undergo KYC, so they will know who you are. no matter how many routes your crypto takes before getting from your private wallet to the exchange wallet, if the exchange knows you are John Smith, they will know it's John Smith's coins that were just deposited in his account. CEXs also co-operate with chain analysis companies to de-anonymize their customers.   

If you haven't gone through KYC but taken part in CoinJoins or coin mixing, that might be a reason for the exchange to ask you to identify yourself depending on what they consider to be taint. Have you tried using Bisq, a completely decentralized exchange that runs over TOR?