Which contact details your website prints

You control which phone number and email address the public site is allowed to show. Anything you leave off is still on your account and still reaches you through the contact form; it simply is not printed for anybody to copy. If you have representation, most actors show the agent and not themselves. If you do not, an email you check is better than a phone number you do not answer, and a contact form is better than either for keeping your address out of scrapers.