This thread is not about privacy from other private citizens/companies, but privacy from the state authorities. For example, my bank account is private in the first sense (even my parents couldn't find out how much money I have unless I tell them), but it's not private in the second sense (financial authorities have the right to ask my bank how much money I have).
But most homeowners don't have the house in a trust. That's mostly a rich-people thing. The default is that it's your personal name(s) on the documents, including in e.g. county tax records.
Perhaps a relevant different example I've seen sometimes is that in some markets for tax reasons developers who build larger buildings (offices, apartments) will make a separate LLC for each building, so when they want to sell it, the title to the real estate doesn't change hands (it still belongs to the same company) but rather they sell the whole "company" instead with the building as its main/only asset.
Last time I sold a house, the only reason I met with the buyer directly was because I didn't use an agent for the sale.