Augusta (1788-1851) was the daughter of King Maximilian I Joseph of Bavaria and his first wife Marie. She was married to Eugene de Beauharnais, the stepson of Napoleon.
Like it's said in one of the above comments, this name was already borne by King George III's mother, as well as his elder sister (who was, by the way, mother to later queen Caroline of Brunswick). But yeah, Augusta was probably only popularized by George III, since he was the King (as opposed to a 'mere' prince and princess of Wales).