In general, property tax and ownership data is public. You can somewhat increase your privacy by purchasing property under a business name, but business formation documents are also public for the most part.

For example, I can go to the website of my county’s registrar and pull up the formation and renewal documentation of my LLC with just a last name.

I don’t think you can effectively hide ownership of property without a shell corporation. The Corporate Transparency Act passed in 2021 requires you to provide ownership records to the treasury but I believe that ownership of the corporation can stay anonymous to the general public.

It's doable, but the general consensus seems to be it's not worth doing - anyone who wants to dox you for the purposes of legal matters will get it anyway, and that's the biggest reason it's usually discussed.

If you're just trying to keep yourself off the Internet, just change your name to John Smith or Michael Jackson.

At least in the US, it's very common to for major assets (especially real estate), owned by a trust.

Although a trust is different from a corporation in many ways, they're similar in that they are both legal entities distinct from the people involved (and can both have their own tax ID numbers, also distinct from those people). They're primarily created for estate planning purposes, but public records will typically show only the name of the trust, not the people who live there.

I tried it, it has no data from my zip.

When I go to a free people search website (I usually use fastpeoplesearch.com) and search for myself, the only accurate information there is from real estate data (and USPS address changes). But reading the article, I have reason to believe that if we were to pay a people finder website, it could be having better data sources such as credit file header information.

Hmmmm, so I should be doing USPS change of address every year or so to random apartments in various locales.

This doesn't seem very comprehensive. As far as I'm aware, every county publishes this information. If I go to my own tax authority's website and search for myself, all of my property tax records come up. But if I enter in my name here, only one state shows up and whoever this is is not me. My name is pretty common, too, so this guy is definitely not the only US homeowner other than me who has this name.