Who can search for me on Facebook?
Facebook takes privacy concerns seriously, including when it comes to your search activity.
Everyone, except people you've blocked, can search for you and click on your profile, but what they can see about you in search results depends on what's shared with them.
Search results respect your privacy settings, whether it's info you’ve shared or posts with tags of you that others have shared. You can adjust what others can see on your profile and timeline, and who can see the things you share.
Keep in mind that posts and photos you've hidden on your timeline are still visible to the audience they're shared with in other places on Facebook, like News Feed and search. Learn more about how you can control what people will see on your profile and timeline.