I mean, yes, but not really. As soon as you transfer your funds from a recurrent wallet to a exchange they can link your address to your name and address, and if, say, the police ever asks for information about you they might have, you're done. Here's where bitcoin mixing services come into play, there's a nice niche for these, but they are also not very reliable.
Privacy is but a myth otherwise.
- Use a P2P platforms instead of centralized exchanges that asks for KYC
- If you ever need to use a centralized exchange, check if they allow withdrawal for unverified accounts first
- Use services that further increases your online privacy such as VPN's and Tor
Other practices to increase your privacy:
- Maintain different wallets for storage, trading, and spending
- Use non-custodial wallets, preferably open-source