Parker - When you say Google will find it, I would expect that. But it will find it and identify myself as the owner? I want it found, I just don’t want it to have my name attached. Nothing illegal is being promoted, just a very sensitive subject matter.
No search engine will identify you as the owner unless you link yourself to it in some way. Assuming it’s on shared hosting, the IP address will be suitably vague and other info that can be found will be largely technology behind the build, where hosted and so on. If you have a company or trading name be sure not to mention it.
The “privacy option’s” can vary greatly on “how private they are”. These are individual companies that listing themselves in the ICANN registry and keeping you “anonymous” to the public. I know of a few hosting companies private option can easily be hacked.
Also if you ever need or want to move the domain, you have to remove the privacy option during the transfer.