What is the name of that type of cap?
It's a flat cap, colloquially more commonly seen as "newsboy cap" in North America. Other areas will have other common names for it, including (as seen on Wikipedia) "scally cap," "bunnet," "Dai cap," "paddy cap," "cheese-cutter," and "driving cap."

You're most likely to find patterns or instructions under the names "flat cap," "newsboy cap," and "driving cap."