To add or remove your profile from the Yahoo! Member Directory, go to My Profiles. Click the "Edit" link next to the name you want to add. On the profile's edit page, click the "Edit Profile Information" link in the yellow edit bar, then scroll down that next edit page that shows up. Check the box next to "Add this profile to Yahoo!'s searchable Member Directory." If you want to remove your profile from the directory, uncheck the box.
Click the "Finished" button to put your change into effect. Your profile will be added or removed within 24 hours.
Adding your profile to the searchable Member Directory is your choice. However, even if you are not listed in the directory, people can still view your profile in Yahoo! Chat, Message Boards, or in other features. In other words, anything you add to a profile should be considered publicly viewable.