This wiki is constantly referring to the penguin as oswald COBBLEPOT but if you look at episode 15 of season two around 21:50 you can see that it is spelled KAPELPUT on his mothers grave.
They might have changed it due to pronouncing it wrong. Where she is from it is easier to pronounce it cause it originates there, and in the u.s, its prone to be said wrong.
The show wouldn't have made a mistake for his name. I think that its fine if it´s cobblepot. It shows that in the interviews, some script, and captions.