This hat category goes by various names. These days most people call these newsboy hats or newsboy caps. Some refer to the larger profile (or diameter) version as apple caps or big apple hats or caps. Inside the cut-and-sewn headwear business, the preferred name is eight-quarter cap as the hat is made by sewing together eight pie-shaped panels and affixing a button at the vortex. In the UK, people call them baker boy caps.
Whatever name you choose to use, we are quite certain that for value and selection, no one does this category as well as us.