Ya well--I'm still gonna call my sweat beanie my skull cap.So far, this is what I've determined in my investigation:
A bandana is just that. It can be used in many ways. If it's folded up and tied around the head, with the top of the head exposed, it's still just called a bandana.
If it's done in such a way that it covers the top of the head, it's called a do-rag. It's not Doo rag, or due rag, but simply Do Rag. Apparently there was a time when the hair on your head was called a "Do", as in Hairdo. This style is also called a "head wrap", or "bandana head wrap", as sold on Amazon. AND, any piece of cloth tied up and used in this fashion is a do-rag. It doesn't have to start out as a bandana.
A skull cap is a form of helmet, with a hard outer shell but may or may not be DOT approved. Half helmets are commonly called Skull caps. Other terms that seem to mean the same thing are "Brain Bucket", "Head Shell"
in doing this investigating, I was hoping to find a place where I fit in. But apparently not. What I wear is called a sweat beanie and doesn't fit into any other category.
I use a black marker to black out the logo and the EVS on the side. Because that's what posers do. :dunno:
When looking for it, I call it my "head gear".