Your profile is privacy level red-- very private. The public-- i.e., anyone not on your Trusted List-- cannot see the name of your mother.
YOU are seeing it because you're looking at the "private" view. If you click on the far-left tab, you'll see what the public sees, and you'll see that whether looking at your profile or your mother's (which I can't even see), that only you can see her maiden name.
THAT said, you want to make sure then, that HER father's profile-- even if he is deceased-- is also private.