If you receive XMR from a KYC exchange, they don't know who sent it to you, only that you received XMR. If you send XMR from a KYC exchange, they will know the address you are sending it to & the amount, but nothing beyond that. They really have no idea what you are using it for unless they ask you and you tell them.
Traders wouldn't want their exchanges to know how much XMR they've received & sent or their dates. They'd prefer to keep their deals private but if a privacy coin doesn't give it they do it outside the centralised exchange. If ppl want privacy I'd ask them to use any DEX.
I'm not sure there's any "decentralized" exchange for XMR. Maybe AtomicSwap supports it but I'm not sure, and they've had troubles recently. ThorSwap doesn't support it at all. There are only KYC exchanges, non-KYC exchanges, and swapping services (a mixture of KYC and non-KYC).
Exch.cx
Bisq
UnstoppableSwap
Exch.cx XMR rates are the highest I've found. UnstoppableSwap's the lowest.