That's one identity, but the owner of the house would have other identities. The fact that you know that the owner of the house approved the lien would not automatically tell you that, for example, the person living in the house approved the lien. Or that a certain employee of a certain company approved it. These would all be separate identities, even if they all refer to the same person.
Even in countries with unique, centralized identities, you don't go around handing your government ID to everyone you meet. You use it for official legal business only. In other contexts you still have less formal identities which remain separate from your official identity.
Also, as a counterpoint, most countries have much stronger centralized identities than the USA, and much less trouble with identity theft.