“How do I block people from finding my profile from doing a Facebook search?”

Here’s how to stay out of public searches in Facebook:

Change your online status to offline. This is probably the easiest way to block a friend from chatting with you. By going offline you will be invisible to everyone and stop receiving chat messages from all confirmed friends.

If you would like to remove a friend, navigate to the person’s profile and click the "Remove from Friends" link at the bottom of the page.....

If you deactivate your account from the "Deactivate Account" section on the Account page, your profile and all information associated with it are immediately made inaccessible to other Facebook users. What this means is that you effectively disappear from the Facebook service.