Yes, you can if you want to. You can completely hide your identity that didn't directly link to anyone's personal identity. But if when it comes transaction there is a possibility that can be traceable or can be tracked. I heard there are services offered who can track Bitcoin transaction in illegal use or any cybercrimes related cases. Chainalysis can investigate and provide blockchain data that possible transactions can be tracked.

So, if you want to protect your personal identity and privacy in Bitcoin transactions you need to do the hard task, and these what you need.

• Use Bitcoin mixing service
• Use TOR to stay anonymous
• Buy/Sell Bitcoin in cash, not on exchange that required KYC
• Use VPN to protect your IP address
• Use New Bitcoin address for every transaction

This might improve your anonymity.