But if the owner is anonymous, how does the country know who to ask for paying the taxes? How would the county even find out that the house changed ownership?

In the grandparent example, it seems the new owner is a trust, which is also liable for paying the taxes (or there can be action taken against its property i.e. the house), but the person owning/controlling that trust is obscured.

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.

<thumbsup> Proposition 13 likes this.

They don't need to know. If the property tax isn't paid a local judge just writes up a new deed to whomever pays off the delinquent property taxes. It is literally property in their jurisdiction. They can take possession any time.