What's the name of the coat with a hat?

A coat with a hat is called a sweater.

"Sweater" was born in new york, USA in 1930s, when it was a tool for cold storage workers. Sweater combines fashion and function, comfort and fashion.

Sweater style:

Women's sweater

The styles of women's sweaters are pullovers, open-chest shirts, slim, long shirts, short shirts, sleeveless shirts and so on. Mainly in fashion and comfort, mostly in leisure style.

Men's sweater.

Men's sweater styles include pullovers, corsets, long shirts and short shirts. Mainly in fashion and comfort, mostly in business leisure and sports leisure style.

Sweaters are only used as daily casual clothes, not as men's formal clothes.