You can always shield (anonymize) your crypto by depositing it in your Incognito account. But if you bought it somewhere else, there’s likely a record of it.
If you want to buy crypto anonymously, use the Incognito DEX. With transaction fees lower than nearly any other popular blockchain, and totally decentralized confidential trading, it’s never been this affordable or safe to buy BTC, ETH, XMR, etc. privately.