The fabric hat is reversible so you can a brown or red hat
I would hazard a guess that the hat is a medieval style, the kind that would normally be made from wool.
The hat is basically a square bag, that follows the shape of the head when worn and leaving 4 corners at the crown where there is an air pocket above your head.
Many shapes of historical hats do not have names, you could call it a beanie of shorts
I would say this hat suitable for any period from at least the 13th to 18th century.
