Remove full name from login window
Is this in the list of previously logged in users?

If you're selling your MacBook, you should consider re-installing the OS with a clean slate, rather than potentially leaving items behind.

You might find there's still a userid on the computer somewhere; you can remove it by running sudo dscl and then ls /Local/Default/Users to see if the username shows up there. delete /Local/Default/Users/name should get rid of it.