I haven't seen an online exchange that doesn't require you to verify before allowing you to cash out. Even if such an exchange would exist you're still sending money to a bank account that's in your name. You have to be extremely naive to think that your fiat can't be traced by your government.
I use exchanger which does not require registration. Of course if I send money to my Bank card that I can detect but I do not. I buy everything that I need in the online store. There you can pay by credit card. I send Fiat from your anonymous account once in the store. In this case, I have no way to track.
Care to give us some more info? I haven't encountered an exchange that would allow me to sell BTC for fiat without verification. Nowadays it's hard to find one that allows trading crypto pairs without at least a basic verification by phone. That's because of anti money laundering and anti terrorist laws. In Europe and the USA it's a normal thing.
Also, sending things to your home doesn't make the transaction anonymous anymore, even if you use a fake name.