When someone searches for your profile on search engines (Google, Yahoo and Live for example) they'll hit your public search instance (that includes a thumbnail, your name as recorded on Facebook database, your regional network etc'). That's apparently what happened in the situation you mentioned. You can easily keep your online privacy by avoid having your public search listing crawled (and thus shown) by search engines. Please follow these steps in order to do so:
1-Login to your Facebook account
2-Hit Privacy
3-Hit Search
4-Now deselect the following statement: "Create a public search listing for me and submit it for search engine indexing."
5-Hit Save
Voi'la you have just made sure that your profile won't be showing up on search engines. If for whatever reason your profile is currently showing up on Google, Yahoo or other search engines, and you want to remove it from the search engine results, i recommend that you execute the above mentioned procedure. Then allow a month or so to have it removed from the search engine result pages.
"TRICK-- avoid having Your Facebook profile indexed by search engines"
Reference : avirtualexit.com
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