A clergyman's square hat is commonly referred to as a "sotana" or "cap." In some contexts, especially within the Catholic Church, it may be called a "zucchetto" or a "skullcap," but these are typically round rather than square. The square-shaped hat is often associated with the academic attire of clergy, particularly during ceremonial occasions.
party hatwitch hat
It is sort of shaped like a hat or an Easter bonnet.
When the moon is shaped like a ball it is called a full moon.
The most common shape for a party hat is a cone.
Glengarry
cloche hat
beret
The "cloche" was a popular bell-shaped hat in the 1920's. Cloche is also French for bell
The boat-shaped hat worn in Scotland is called a "balmoral" or "balmoral bonnet." It is typically made of wool and has a flat, square top with a pom pom in the center.
Glengarry
One name its called is hermione.
Cloche Hat
fascinator
A good choice for someone with a heart-shaped face is a tilted, asymmetrical hat.
The different styles of marching band hats have different names. The typical hat, which is shaped like a bucket and has a plume on top, is called a Shako. The style which resembles a "three musketeers hat" is called an Aussie.
One can probably get a hat shaped like a penguin at an aquarium souvenir shop. One is more likely to get this style of hat if the aquarium features penguins.