cravat is borrowed from French cravate, which is a use of Cravate "Croat, Croatian". The OED tells us that cravats were worn by Croatian mercenaries, and the style was adapted by the French in the 17th century:
It came into vogue in France in the 17th c. in imitation of the linen scarf worn round their necks by the Croatian mercenaries. When first introduced it was of lace or linen, or of muslin edged with lace, and tied in a bow with long flowing ends, and much attention was bestowed upon it as an ornamental accessory. In this form it was originally also worn by women. More recently the name was given to a linen or silk handkerchief passed once (or twice) round the neck outside the shirt collar and tied with a bow in front; also to a long woollen ‘comforter’ wrapped round the neck to protect from cold out of doors.
French cravate was borrowed from German Krabate, borrowed from Serbian/Croatian Khrvat/Hrvat. Croatian Hrvat was adapted into modern Latin Croatæ, then borrowed into English as Croat.