coif (n.)youdaoicibaDictYouDict
late 13c., "close-fitting cap," from Old French coife "skull-cap, cap worn under a helmet, headgear" (12c., Modern French coiffe), from Late Latin coifa "a cap, hood" (source of Italian cuffia, Spanish cofia, escofia), of West Germanic origin (compare Old High German kupphia, Middle High German kupfe "cap").
eye-shade (n.)youdaoicibaDictYouDict
also eyeshade, 1808 as a type of headgear, from eye (n.) + shade (n.).