What's the name of this hat? An old black hat with wings on both sides.

This is called "Shantou"

Tou (fútóu), also known as folded towel. Also known as flexible packaging. Soft towel for Baotou. Because the gauze used in Shantou is usually cyan and black, it is also called "black gauze". Later generations are commonly known as "their duties." ? The legend began in the Northern Zhou Dynasty. Originally called Potou, it was called Shantou in the Tang Dynasty. At first, it was made of gauze, but later, because it was soft but not hard, it made a hawthorn shirt out of tung sawdust and raised the top in the gauze. When you wrap a hoe, you can tie two knots in front of your forehead, and tie them into two feet at the back of your head, which naturally hangs down. After canceling the front knot, use copper wire as a stalk to prop up the soft foot and turn it into a hard foot. The emperor of the Tang Dynasty bent his feet with a hoe, and the ministers of the people hung their heads. The five dynasties gradually straightened out. In the Song Dynasty, Shantou was called "Shantou Hat" with rattan towel as lining, yarn as table and pigment, which could be taken off at will. Its styles are right angle, local foot, cross foot, sky, downwind and so on. Different identities have different styles. The emperor or bureaucrat stretched out his feet and stretched them straight to both sides. Servants with low status wore footless hoes.