When someone searches for your name on search engines (for example Google or Yahoo) they can find your Facebook public search instance ( which includes a thumbnail, your name as recorded on Facebook database, your regional network, friends etc).
You can avoid your public profile to be crawled by search engines, so people won’t find you anymore.
In order to do so, please follow these steps:
1. Login to your Facebook account.
2. Go to Settings -> Privacy Settings. (see image below.)
3. Select Search. (see image below.)
4. Deselect the following checkbox: “Create a public search listing for me and submit it for search engine indexing.” (see image below.)
5. Press Save Changes.
In about a month or maybe less your profile will be removed from the search engine result pages.