The mask's name likely references the Spanish, fictional libertine of the same name who was renowned for his skills of seduction and his hypersexuality. The term 'Don Juan' is also Spanish slang for 'womanizer.'
Don Juan may also be a reference to the actor who played 'Sonny' in Miami Vice, Don Johnson.
In the game PAYDAY 2, there is a wearable Don Juan mask that has a "protip" in the description. The tip says the mask provides 2200 points when performing ground executions against a wall.