Don't Get Personal (1942)

Elmer Whippet inherits the Whippet Pickles company and sets out to meet the two stars, Mary Reynolds and John Stowe, of the radio program sponsored by his company, as he thinks their on-air quarreling is real. Two former associates, Jules Kinsey and J.M. Snow cross him up by substituting Susan Blair, an office secretary, for Mary and Elmer thinks the show's writer Paul Stevens is John.