Recent changes to the Facebook privacy settings, has made it difficult for users to conceal their personal profiles, as Facebook has removed the ability to hide from public search. Facebook profiles have the ability to be located through the Facebook search function and in some cases via search engine sites such as Google.
However there is some reprieve. Within the Facebook Privacy Settings, you have the option to remove yourself from a search engine link. This means that persons using a search engine to look for you via a name search, should be unable to link to your Facebook profile.
Go to > Privacy Settings > Who Can Look Me Up? > Do you want other search engines to link to your timeline? > Uncheck the box. (as per diagram below)
Be aware this may not remove a link to your profile due to any public content that you post. As a result please ensure you check your privacy settings and only post your information to friends.