You have to type it exactly as their name actually is if they're offline. So if someone's name is "LiciaMango" you cannot type "Liciamango" or "liciaMango", or any version like that. It has to literally be typed "LiciaMango", or else it will never register who you're actually trying to remove from your friends list.
That's really the only problem I've ever seen someone have with removing their friend, they simply didn't type the name exact.