You can't delete that information without replacing it with something. If this profile does need to be re-purposed as Naomi Leeper and not Albert Shaw Leeper, you'll have to replace several bits of information.
So for example, if her name is Naomi, what I would do is:
Replace Albert with Naomi in the Proper First Name field
Replace Albert with Naomi in the Preferred Name field
Switch from Male to Female
Go to the biography, and replace "Albert S. Leeper" with "Naomi S. Leeper".
I'm hoping I found the right profile for this, but not sure - I went to:
Is that correct?