What is a bed that folds into a couch called?

A bed that folds into a couch is called a sofa bed. It's also known as a sleeper sofa, sofa sleeper, pullout sofa, sleep sofa, couch bed or hide-a-bed.

During the day, the sofa bed functions as seating. For sleep purposes, the cushions are removed, and the bed unfolds via an opening mechanism that allows the user to lift the bed up and out.

Sofa beds come in various sizes, including chairs that convert to single beds and sofas that provide seating for three people and open to queen-size beds. A sofa bed mattress is about half the thickness of a standard mattress and is usually constructed of springs or foam.