“Who can look up your Timeline by name?” Anyone you haven’t blocked. Facebook is removing this privacy setting, notifying those who had hidden themselves that they’ll be searchable. It deleted the option from those who hadn’t used it in December, and is starting to push everyone to use privacy controls on each type of content they share. But there’s no one-click opt out of Facebook search.
To be fair, the “Who can look up your Timeline by name?” feature was likely misunderstood by lots of people. At first glance, you might assume it means that strangers can’t find your profile. But that’s incorrect. There have been lots of ways to navigate to your profile, like clicking your name on a photo you’re tagged in, finding your name in a friend’s friend list, or combing through Likes on a mutual friend’s News Feed post.
With the roll out of Graph Search, the avenues for sniffing out someone’s profile grew exponentially. Basically every piece of personal information (and soon the content you post about) could bring you up in a search. If you publicly list that you live in San Francisco, a Graph Search for “People who live in San Francisco” could lead someone to your profile.
James' World 2 