What can I trade with bitcoin without having to give out private details like name and address? (Imagine I don't even have a name or address.) I'm looking for stores of value like gold or stocks. Naturally litecoin and other cryptocurrencies fit, but I'm looking for more than that. And alpaca socks, though they may be durable and resalable, may lose value after a perception of being "used", and therefore are not a good store of value.
Over a reputable, lisenced exchange? Nothing. They all require KYC (know your customer) laws to put friction in money laundering, with the exemption of Swiss based Vaultoro.
What you want is to find someone on localbitcoins.com who will meet you in a cafe or restaurant or somewhere and swap bitcoin for whatever you want, dollars, gold bars, diamonds, art, or whatever else. You call ask to meet at a place that can verify the transaction ( for example, if you wanted to anonymously buy art with bitcoin, you could ask to meet at an art gallery).
No reputable online exchange will provide this service, except vaultoro will give you gold anonymously (since they are based in Switzerland which does not have strong KYC laws.)