By default, Facebook allows any user to find you in the search results. If you would like to keep things a little more private, you can configure your privacy settings to narrow the amount of users that can find you when searching with Facebook.
1. Go to Facebook and login to your account.
2. Go to the upper right corner of the page and select privacy.
3. On the Privacy Overview page, select Search.
4. Use the Which Facebook users can find me in search? dropdown to select the desired value. The choices are Everyone, All my networks and all my friends, Some of my networks and all my friends and Only my friends.
When you choose a value other than Everyone, checkboxes will appear beneath the dropdown allowing you to further control who can find you in the search results.
5. When you have finished, click the Save button at the bottom of the page.