From Muppet Wiki

Malcolm Monster is the protagonist of the book Where's My Blankie? Malcolm lives on Sesame Street with his sister Monya Monster and his parents. Malcolm is incredibly attached to his security blanket, an old quilt which he takes everywhere. The quilt was a baby gift to him from Grandma Monster.

As the blanket grows shabbier, and Malcolm grows older, his parents try to persuade him to leave it at home. Still, he insists on taking his blankie on a trip to his grandparents, and Monya teases him, calling him a “baby monster.” At the end of the trip, Malcolm finds that he forgot his blanket. While initially disconsolate, Malcolm waits for Grandma to send it, and is gradually distracted by other activities with his friends. By the time the blankie arrives, he has completely overcome his dependence on linens.

Both Malcolm and Monya re-appear in The Monsters' Picnic.