Although not created the 20th century, this drink probably takes it's name from Mary I, Queen of England (1553-1558) who became notorious for her literally 'bloody' persecution and execution of Protestants.
Many sources credit Harry MacElhone himself with the creation of the Bloody Mary. The following information is more likely correct.
"The Bloody Mary was created by Fernand "Pete" Petiot, a bartender at Harry's NY Bar Paris, and he was brought to NYC shortly after repeal of prohibition to work at the King Cole Bar in the St Regis Hotel. The name of the drink was changed to the Red Snapper for a while, but eventually it was again known as the Bloody Mary.”
(source: Gary Regan, Ardent Spirits)
Using a celery stick to garnish a Bloody Mary originated in the 1960s at Chicago's Ambassador East Hotel. An unnamed celebrity got a Bloody Mary, but no swizzle stick. He grabbed a stalk of celery from the relish tray to stir his Bloody Mary and history was made.