Check if your domain registrar offers an anonymous registration service. Mine provides it for free, but some charge a small yearly fee. It is still fine per ICANN standards since it simply goes to a forwarding service.
While most registrars would be perfectly fine, I worry about the one that is willing to take the domain for themselves (for a domain not worth going to court over).
While not exactly what happened, I remember the case of the @N twitter account be stolen (https://medium.com/@N/how-i-lost-my-50-000-twitter-username-...), and wonder if having your actual information on the registration would help or hurt a situation like that.