Break the trail from your identity.
The privacy of a deposit is only as good as the coin that funded it. Coin bought from an identity-checked exchange and sent straight to the market ties your name to the deposit.
If you hold Bitcoin, swap it to Monero inside a wallet like Cake, which breaks the direct exchange-to-market link.
Buy coin from another person with a random identity rather than a verified account. Either way, route through a fresh wallet you control before depositing.