I was unaware that Monopoly’s avuncular, top-hatted and mustachiod mascot even had a name, but apparently he does — indeed, he has had two! The original 1935 edition of Monopoly featured the character on Chance and Community Chest cards and he also made a cameo appearance in the game Dig published in 1940.
However, it wasn’t until Parker Brothers’ publication of the game Rich Uncle in 1946 that he got a name: Rich Uncle Pennybags. Mr Pennybags (first name: Milburn) has been a feature of Monopoly for the majority of its 75-year history, although in 1999 he was rechristened, rather prosaically perhaps, Mr Monopoly.
The original game has spawned a global brand and thousands of individual products, which must, I think, make Rich Uncle Pennybags the most recognised boardgaming icon in the world. As always, Wikipedia has more information.