It varies.
There are some states where you - the public - are not able to determine who a property owner is via search results. This has pros and cons.
However, the Government, County, State, and Federal, know who owns the land.
California is the most notable one. The reason is, I believe, that government officials legally cannot have their names appear in those search results with the address, and due to the impossibility of tracking that counties in CA, they just don't show both the name and address. Also, California is just one of the worst states to search for title stuff. A little digression, but it may help a KFer in the future.
Florida and TX sometimes have confidential properties. A few other states do too but TX and FL are the biggest; I believe they block out military and law enforcement. Some county sites have holes/bugs where you can trick the system into spitting out the confidential information--unsecured PDF generator plugins.
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Also, third party vendors however may have this information and are either plugged into county systems already, or have done their own tracking. Back when I worked with this stuff there were tools where you could search by name or address and get accurate info. So even you're not safe there.
So you're saying there is no recourse to stay hidden as a property owner?
There might be. You'd have to talk to a lawyer, there is probably some complicated arrangement on how this would be done, but for the average person, if you want to hide, you might want to rent it. Don't let them tell you the trust is enough if you're gonna ever possibly have to sign any docs with your own name at the county and have them recorded. As you can see, if Tim intended the trust to give him privacy, it was a waste--it took me less then 3 minutes to find him on the recorder site.
Many states have assumed spousal joint tenancy when married, so you could marry someone in secret and have them hold the house, and you legally get de facto ownership of it. Maybe something else will come to me. But, even still the bank will want you to sign off on the mortgage because you have title to the house. Everyone with title to a property must sign off on the loan in most circumstances.
If anyone ever has any questions, feel free to PM me. I'm very, very good at this, using these recorder and assessment sites, among others.