The name Naugatuck is said to be an indigenous term (in the native American Algonquian language) for either “one tree” or “fork of the river.” "Naugatuck" was also the name of a village of the Paugussett sachemdom on the Naugatuck River where Naugatuck Connecticut is today. Another Paugussett sachemdom village (Capage) existed on the Naugatuck River a few miles south at what is now Beacon Falls, Connecticut.

Naugahyde is a brand of artificial leather (or "pleather" from plastic leather. It was developed by United States Rubber Company, and named for the Borough of Naugatuck where it was first produced.  A marketing campaign of the 1960s and 1970s asserted humorously that Naugahyde was obtained from the skin of an animal called a "Nauga". The claim became an urban myth. The campaign emphasized that, unlike other animals, which must typically be slaughtered to obtain their hides, Naugas can shed their skin without harm to themselves.