The name, also spelled paw paw, paw-paw, and papaw, probably derives from the Spanish papaya, perhaps because of the superficial similarity of their fruit. Pawpaw has numerous other common names, often very local, such as prairie banana, Indiana (Hoosier) banana, West Virginia banana, Kansas banana, Kentucky banana, Michigan banana, Missouri Banana, the poor man's banana, and Ozark banana.

The earliest documentation of pawpaws is in the 1541 report of the de Soto expedition, who found Native Americans cultivating it east of the Mississippi River. The Lewis and Clark Expedition depended and sometimes subsisted on pawpaws during their travels. Chilled pawpaw fruit was a favorite dessert of George Washington, and Thomas Jefferson was certainly familiar with it as he planted it at Monticello. The Ohio Pawpaw Growers' Association lobbied for the pawpaw to be the Ohio state native fruit in 2006; this was made official in 2009.

Growers hope that potential medical use will eventually lead to increased market demand from the pharmaceutical industry. The seeds also have insecticidal properties. Some Native American tribes dry and powder them and apply the powder to children's heads to control lice; specialized shampoos now use compounds from pawpaw for the same purpose. While it is not meant to replace conventional cancer treatments, pawpaw extract is currently investigated as an alternative cancer treatment alongside conventional and approved treatments, partly due to inhibition of ATP production by acetogenins.