Here are some classic films stars and their real birth names:
Rita Hayworth = Margarita Carmen Cansino
Cary Grant = Archibald Leach
Barbara Stanwyck = Ruby Katherine Stevens
John Wayne = Marion Robert Morrison
Lauren Bacall = Betty Joan Perske
John Garfield = Jacob Julius Garfinkle
Veronica Lake = Constance Frances Marie Ockelman
Tony Curtis = Bernard Schwartz
Mary Pickford = Gladys Louise Smith
Kirk Douglas = Issur Danielovitch
Weren't these fun!? I can see now why many did change their names but many like Lauren Bacall still went by their birth names when it came to close family and friends. Today she still prefers to be called Betty.
The changing of the names is a reminder of how much control the film studios had on their actors and also how powerful a name can be in changing ones images or public persona.