A handkerchief is literally a "hand-head-cover" — kerchief means cover-head from French, and adding hand- specified you held it rather than wore it.
A piece of cloth used to cover the head; a square scarf worn on the head or around the neck.
From Anglo-Norman courchief, from Old French couvrechief, a compound of couvrir (to cover) + chief (head), from Latin cooperīre (to cover) + caput (head). A kerchief is literally a head-cover. Key roots: caput (Latin: "head"), cooperīre (Latin: "to cover").
The handkerchief is literally a "hand-kerchief" — a kerchief held in the hand rather than worn on the head. And kerchief itself literally means "cover-head" (from Old French couvrir + chief). So a handkerchief is etymologically a "hand-cover-head" — a head covering that you hold in your hand, which makes perfect sense only once you know the history. The word chief in English