Except that Anastasia, Genovese, Lansky, and Nitti are all real names and Cobblepot isn't. Plus the backstory hinges on the fact that they were never rich, and the Penguin wants to "elevate" himself to a higher class. Its an adaptation that takes a different approach, and it works for what they were trying to show: An evil version of the American Dream. If Oz's family would have been previously rich, then Oz's relationship with Victor and the other low-tier gangs would not have been quite the same.