I think they should have seperate public and private photos and names. At present there is only a public option for 1 photo and full name. It would be very helpful if there was a seperate private photo. That way I could use some graphic for the public photo and have a photo of myself only visible to people I share with (mutual followers). I am not going to my a photo of myself in the public profile.
Similarly, there should be an option for "full name" to be made private instead of public. My handle could suffice as my public name I am not putting my real name in the public area. If I wanted to do that, I would have just joined Facebook.
Excellent idea!