Note to the Village People: The lyrics in your biggest hit need an update. The organization previously known as the Y.M.C.A. is henceforth to be called “the Y.” One of the nation’s most iconic nonprofit organizations, founded 166 years ago in England as the Young Men’s Christian Association, is undergoing a major rebranding, adopting as its name the nickname everyone has used for generations. “It’s a way of being warmer, more genuine, more welcoming, when you call yourself what everyone else calls you,” said Kate Coleman, the organization’s senior vice president and chief marketing officer.