The mountain hat, the Campaign Hat, the Montana Peak or the Smokey Bear.
Call it what you want the origins of this hat can be traced to the 1840s when army troops posted in the west took to wearing civilian hats which were far more practical than the shakos or kepis then in vogue with most western armies. The name campaign hat started to be used after the 1872–1876 regulations which introduced a black felt hat for fatigue which use was derived from the types popularised during the American Civil War.
The notable crease we see today was apparent as early as 1893 and the re-crease into a further point was actually introduced by British South Africa Company scouts in Africa in order to keep the rain off. Three years later in 1896 these same scouts introduced the hats to a British Officer Sir Robert Baden-Powell which in turn influenced the Canadian troops which served below him. The ‘Montana Peak’ was officially adopted by the army for its peaked design in September 1911 and given the name 'Campaign Hat’