A Havelock is not a hat, it's a hat cover or to be more accurate a helmet cover
Mainly used by the military to change the look for say a blue UN peacekeeping or to a different camouflage pattern of the helmet without the need to repaint or swap helmets.
Havelocks get their name from the British General Henry Havelock, invented originally to protect the wearer from the sun.
The image below Before and After the cover was fitted
