Fez
* rounded brimless cap fitting the crown of the head * the dome of the skull
Liberty cap is a type of hat. It is a soft brimless conical cap.
could be a watch cap or a skullcap maybe even a slough hat
The distinctive headgear of a shriner is a red fez, a kind of brimless conical cap.
The Scottish brimless wool cap is called a "Tam o' Shanter," often simply referred to as a "Tam." It features a rounded, flat top and is typically made from wool, often patterned with tartan. The cap is named after a character in a poem by Robert Burns, and it is a traditional part of Scottish attire.
Looking somewhat like a beret, that would be a Scot's bonnet, or tam-o'-shanter. COULD BE A GLENGARRY
The hat is called a fez. It is normally found on the souks of Morocco and worn by men on special occasions.
A Fez
toque
A CAP is a brimless head covering with or without a visor. Examples: a Baseball cap has a visor to protect eyes from the sun; a ski cap is a knitted head covering without a visor.A HAT is a head covering, usually with a crown and a brim. Examples: a fedora has a crown with a crease and a brim; a top hat has a flat top crown and a brim.A visor only extends around the front of the hat while a brim completely encircles the hat.
Moroccan
Medieval monks often wore a hooded garment called a cowl, which covered the head and neck. The cowl had a large hood that could be thrown back or pulled up to cover the head. Additionally, some monks also wore a soft brimless cap called a biretta, which was usually worn indoors or during important religious ceremonies.