Fly Me to the Moon [edit]. In 1960 Peggy Lee recorded the song then made it more popular when she performed it in front of a large television audience on The Ed Sullivan Show.As the song's popularity increased, it became better known as Fly Me to the Moon and in 1963 Peggy Lee convinced Bart Howard to make the name change official.n 1954, when writing the song which would become famous as Fly Me to the Moon, Bart Howard had been pursuing a career in music for more than 20 years.