I spent half an hour when I should have been working trying to find out if there was a specific word for such things. 'Headpiece' or 'hairpiece' was the closest I could find, but I'm not sure if that's right. If there exists a generic word for formal-hat-equivalents, I also couldn't find it. If such a word is needed, I suggest 'isomillinery'.

It suits you, whatever it is.