No celebrity owns the house the live in or stay in. No truly rich person does.
An LLC or more likely a trust owns the house, land, everything they have. And those are owned by other LLCs and Trusts so you can’t follow the chain. If someone is doxxed, they go somewhere else. Many places are rented out (think Airbnb) all the time. If you get caught, your agent will “leak” that’s just where you were vacationing and the next paparazzi photos will be in different locations on purpose.
Then you do what many do, and buy their real homes in countries that take privacy seriously. When you want an escape, you fly to your real house. No such thing as papparazi, security issues, or anything.