It may be hard to determine who's registered a domain name, but if you're doing anything other than simply parking it, there are several points of attack other than the domain name registration (hosting and credit card processing being the most obvious 2).
Hosting is certainly doable with pre-paid credit cards (and sometimes even PayPal).
I'm not sure why this is even relevant anyway - the real problem with enforcing IP rules isn't identifying the person - it's jurisdiction. If a site is hosted outside the US and the domain is registered outside the US, and the country where it is hosted and registered doesn't respect US IP laws then there currently is very little anyone in the US can do about it (easily anyway).
You can use a free host of some sort. You'll get ads, but you'll be difficult to find (tracable to an internet cafe somewhere at most, if you do it right)
