You can create a simple land trust on your own for anonymity, but if you have a complicated structure or have other requirements, you should consult and attorney and have them set up the trust for you.  

Well so much so trying to keep the property anonymous!

Finally, with the use of Trusts while establishing these structures you can add a level of anonymity by removing your name from public record.The LLC, when established correctly, would create a legal stop-gap between the investment and you and your personal assets.

If so, which state is best to keep my name anonymous?

I always suggest consulting with an attorney to create an LLC, it provides protection and anonymity which easily surpass the cost.

That will afford me asset protection, anonymity, and to some extent, tax benefits.

An LLC is useful for two things: anonymity and legal protection.

If you are buying a SFR, you probably don't need this policy until you move and turn it into a rental.Another option I've heard of but not practiced is to acquire the property through a trust (as opposed to or in addition to a LLC) ... this if done carefully may protect your name/identity from being on public record as the owner and may provide some protection through anonymity.

I like LLCs better for my passive commercial holds only, personally.My reasons for having the mgt corp were for anonymity (it has a very generic name) to pay rents to, credibility (new applicants are more ok giving my corp holding monies), having a 'bad guy' I have to check with for tenant requests, ease of p&l/bookkeeping, 1 place to receive all 1099s for HUD and agency pays, one mileage platform to record on (not every property), retirement account options, a way to obtain health insurance if needed, etc.  

Trusts are much better and are totally anonymous (except for deed) and no annual reporting.