Control who can look up your profile (timeline) by name.

Facebook used to have a setting that controlled who can look up your profile (timeline) using your name.
Facebook removed that setting because your profile (timeline) could be discovered in other ways in connection with your name.
For example, if you selected Friends or Friends of Friends for this setting, it only prevented your profile (timeline) from showing up in search results.
It didn't prevent a link to your profile (timeline) from showing up in search connected to other posts, like posts you're tagged in. It also didn't prevent your profile (timeline) from being discovered through other search terms like employment, college, location, etc.
Additionally, anyone who knew your unique Facebook web address (either your User ID or username), could find your profile (timeline).

Many people used this control to prevent unwanted friend requests or messages. To control who can send you a friend request or a Facebook message:

1. Click the account menu at the top right of any Facebook page and choose Privacy Settings

2. Next to the How You Connect heading, click Edit Settings
3. Select your preference from the dropdown menu next to Who can send you friend requests? or Who can send you Facebook messages?