You can’t hide your name from search within Facebook, but you can hide your name from other Search Engines.
Why would you want to hide your name from Bing and Google search?
Well, you may like a certain level of privacy for your Facebook Profile, so that if your name is searched on through a search engine like Google, Yahoo or Bing your Facebook Profile won’t show up and draw people to your Facebook Profile’s Timeline.
Facebook have updated their privacy settings for profiles, so the settings are in different places now.
To untick this option to have your Facebook Profile linked from search engines like Google and Bing. Follow the instructions below:
1. Click on the Cog or Daisy Wheel, move cursor down to Privacy Settings and Click.
Go to Privacy/ Who Can Look Me Up/ Do you want other search engines to link to your timeline. Click Edit and be sure that the let other search engines link to your Timeline is UNTICKED!