This is a Bugatti Cap, essentially a flat cap combined with ear flaps like a trapper hat
It has earlaps that can be worn up making look like a traditional flat cap look or pulled down to warm your ears when the temperatures drop.
More importantly, the ear flaps tie together at the bottom with a button or press stud which keeps the hat on even in strong winds or while you're driving your open-topped sports car
Bugatti caps are normally made of a tweed fabric like this one
I assume although I may be wrong the cap is named after the Bugatti cars which built its first racing car 1905.
