Monogrammed describes a thing that already has a monogram on it. A monogrammed towel has those letter-designs sewn or printed on. A monogrammed shirt has the owner’s letters on the pocket or cuff. It is the -ed form of the verb to monogram, used like an adjective. The design itself is a monogram; the bag that carries it is monogrammed. You will see it on gift shops, hotels, and luxury brands, and it can sound a little fancy. Though actually, people also use it for anything marked with letters even when the letters are not artfully twisted — a picky speaker might say a plain printed “J.W.” is just initials, and a true monogram weaves the letters into one picture.