There is a proper name for those nuts and for the life of me I cannot remember the name. I'll go to the garage and get one out and find the name. They work on the same premise as a molly or a poprivet that is split and I cannot remember the proper name for the poprivet. The nut I'm talking about leaves a treaded piece to use screw to mount with. Back in a moment with the answer on edit.
The correct name is Jack Nut. They are used to create a mounting in thin materials, especially plastics and fiberglass.
linkHere is a site with the rivets called trifold blind rivets. The trifold does not have threads remaining after the rivet is expanded. Much stronger than a plain pop rivet, which by the way were very popular in England before they were here in the US. On looking at the pictures again, I thin what you have is a Trifold poprivet. On first look at the devise that held my door lock actuators on my F150 they looked like they used a screw in the cent wut it was the shank of the poprivet.
I have used Jack Nuts to provide a screw mounting in the filon skin of my Bounder where there wasn't any stud to attach to.