Facebook Search Box generally used for searching peoples to such as friends and get information about people you found interesting. Facebook saved names on the search box when you search about them.
When you search for someone on Facebook by search box including Profile, Page, Group etc. Then Facebook cookies saved that information on the search box.
So, If you want to clear Facebook history including search box history you can easily do it.
Clearing The Facebook Search Box History
Step 1 :
Login in to your Facebook Account using Email Address and Password
Step 2 :
Move the mouse arrow, to the search box and click on it.
Step 3 :
Click on “Clear Searches” to remove all search names.
Step 4 :
In the pop-up dialogue box, again click on the same button for verification propose. Now after completing all the above steps check out