It was invented by Simpson
It represents the rising sun
A slouch hat is a brimmed hat usually made of felt or cloth, it was commonly worn back in the day as part of the military uniform, but in the recent years have become a fashion accessory, for women and men.
If you're talking about an in-game hat, there simply isn't one. But if you're looking for it's name in real life, then it's a sort of mix between a slouch hat, and an akubra. Mostly a slouch hat though.
Cheese Cake by Dexter Gordon
Top Hat grossed $3,202,000 worldwide.
The Cat in the Hat grossed $133,818,283 worldwide.
Green clothing, hat with a cotton ball on the end, pointy shoes, and slouch to look shorter.
Top Hat grossed $1,782,000 in the domestic market.
The Cat in the Hat grossed $101,018,283 in the domestic market.
In Australia's colonial years, the felt slouch hat was adopted by New South Wales for its mounted troops. In 1885, it became part of the uniform of the Victorian Mounted Rifles, and in 1890 the felt hat was then adopted by the military for its defence forces. It was upturned on one side, largely for practical reasons, as during rifle drills, it would get in the way. Upturning the right side prevented this problem, but later it became upturned on the left hand side. There is a great deal more symbolism involved with the development of the slouch hat within each of the states. More information can be found at the related link.
They are a sun hat appropriate for a sunny climate. They were adopted by troops of the Australian Colonies and carried on into the Commonwealth Military Forces.