What you put up in your UNF Domains space rests entirely with you. You can choose not to pick a domain that reveals your name. You can use a pseudonym on your actual site. However, when you sign up through the default process, your name does get published as part of the public record about your domain name. Anyone can find it by looking up details about the ownership of that domain name through a public “Whois” request.
This is NOT an issue if you’re already planning on using your name openly on your site (in your domain name or elsewhere). This option is aimed, specifically, at those who, for whatever reason, feel they want to take every precaution to hide their identity on their site.