Dumb question about how Neuman is pronounced.

I don't think one is wrong and the other right. It's common practise worldwide to pronounce foreign words in a way more typical for the recipient language.

Language is a funny thing, nickname for example comes from the german ekename (other name). What happened was the morpheme boundary shifted from 'an ekename' to 'a nekename' and folk etymology lead to the new word 'nickname'.

How do you pronounce Framus?
 
I know it is, but that doesn't make it that different. Just listen to the commentators on eurosport.