Doris Day, The Pajama Game, 1956.   Two swell singers with the same-sounding name were sought by Warner Bros for the musical  about a strike at a  pajama factory. (Honest). Could be that Head Bro Jack Warner didn’t know the difference between Janis Paige andf Patti Page…  So Janis was free  to steal Silk Stockings from Fred Astaire and Cyd Charisse at MGM – because  the Maker of Great Musicals knew which singer was which! !