How to Delete Names in a Facebook Searchby Rob Harris ; Updated September 28, 2017
To delete a name in a Facebook search, you must block the user whose name you want to delete. The main purpose of blocking a person is to keep him from seeing your profile on Facebook, but it also keeps you from seeing his information. Blocking prevents you from searching for that person until you choose to unblock him -- it deletes him from your searches. Blocking also removes all ties, such as confirmed Facebook friendships and the ability to send messages.
Log into Facebook. In the upper-right corner, click on "Account" and then "Privacy Settings."
Find "Block Lists" in the center of the page near the bottom. Choose "Edit Your Lists."
Enter the name or email address of the person you want to block. Click "Block This User."
Choose the correct person from the pop-up list. Click "Block."
Log into Facebook. Type the name of the person you want to block in the "Search" box at the top of the page.
Click on the person's profile page to open it.
Scroll to the bottom of the page and click on "Report/Block This Person" on the left side. Place a check beside "Block This Person." Click "Submit."