Facebook has removed a privacy feature, which was enabling the users to choose whether to show or not in the search function to other people.

Facebook announced on Thursday that any Facebook users can fin any users in the social network by typing their name in the search bar, but its up to the user to share things with certain people of interest. Users already got the option to share things with certain list of people or they can post updates for the public.
Facebook will show up a notification for every user before removing the feature as shown below:
User, we wanted to make sure you know we’re removing the “Who can lookup your Timeline by name” setting.
This setting controlled whether people could find your Timeline by searching for your name. We’re removing the settings because it isn’t as useful as it was before, and now there are better ways to manage your privacy using your privacy shortcuts. (with a Okay, I understand button)
According to the company, there were only “single-digit” percentage of the 1.2+ billion people on Facebook using this settings till date. But, just imagine 1% is equal to 12 million people, who didn’t wanted to be found on Facebook search!
This removal might help the social network to deeply integrate the user accounts with the search feature of the website and it would help to bring up the search function of the site in easy manner.
[source]