How to Hide Your ID on Facebook
Facebook is the choice of hundreds of millions of users that want to stay in contact with friends and family. In fact, Facebook states that you should only use the site for connecting with people you already know in real life or from another online community. Facebook does not advocate friending people on the site who you do not actually know. Nevertheless, spam remains a problem on Facebook and many people you do not know might try to contact or friend you. To help prevent Facebook spam and unwelcome friending request, hide your ID from Facebook search results as well as those of major search engines.
Open your Web browser and navigate to Facebook.com. Log in with your username and password.
Click the drop-down arrow next to the "Account" label at the top of your Facebook profile page. Click "Privacy Settings" on the drop-down list.
Click "View Settings" on the "Choose Your Privacy Settings" page. After the "Connecting on Facebook" page appears, click the "Search for you on Facebook" drop-down list. Click and select "Friends Only."
Click "Profile" at the top of the page to save your privacy settings. Facebook redirects you to your main profile page. In most cases, it takes a few hours for the privacy changes to propagate through Facebook and other major search engines. After the changes propagate, your personal Facebook ID or username does not appear in search results from Facebook or other search engines, unless the person performing the search is already an accepted Facebook friend.
Article Source: http://www.ehow.com/how_11384043_hide-id-facebook.html