From the experts:
Hard as it might be to believe, Gladys was the Harper of 1900, emerging almost out of nowhere to take the naming world by storm. It became a favorite among parents--and writers of romantic Edwardian novels, seen as somewhat exotic. One impetus was the 1870 Ouida novel Puck, whose heroine was the idealized beauty, Gladys Gerant.
Gladys reached as high as Number 11 at the turn of the last century, popular along with other s-ending names such as Doris. Though Gladys hasn't shown any signs of revival yet, some parents might respond to the 'glad'ness of it, and its gladiola-flower feel.
It's been associated in the U.S. with singer Gladys Knight.