There are many different types of military hats that were worn throughout history. Some had foreign names and others had different names for different types. Here are a few.
Helmet
visor cap
overseas cap
busby
shako
pickelhaulbe
steelhaulbe
pith helmet or sun helmet
crash helmet or flight helmet
a pilgrim hat is called a pilly hat
K-Bar
beret
The collapsible hat, very common in 19th century theatres, was called an OREMA.
A hatter
Ushanka
A military hat is called a cover because it literally covers and protects your head. It's simply just a more formal term for a hat. (i.e. guns vs weapons, bathrooms vs latrines, etc.)
It's called a kepi - pronounced kay-pee.
Mussolini's Territorial Army, called "Milizia" (Militia) wore a black fez.
cap and gown. the hat is called a mortarboard.
a leperchaun's hat :P
It's called a homburg hat
Its called a hat box
According to Irish folklore, it's called a cocked hat.
A guardsman hat is called 'Bear Skin'
it is never explaned why keroro is wereing the hat, but is beleaved my many that it is for military purposes
Its called a Tri-Corn Hat