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Wikipedia is useful here:

> "The Koch family (/koʊk/ KOHK) ..."

https://en.wikipedia.org/wiki/Koch_family

That was the first place I looked, and by its descriptive nature it is indeed useful for ascertaining that people do in fact say "coke brothers". But the question asked was what the actual Koch brothers say.

It was always my assumption that the name "Koch" was pronounced like "coke", with a hard c and silent h as opposed to the ch in church.

It's of German origin, I would have assume it would be pronounced either as such[1], or anglicised with a k as in "stomach", which seems like the most common way for English speakers to deal with the troublesome voiceless velar fricative. Another option is to simply use the English cognate "Cook". "Coke" on the other hand seems far fetched enough that I wondered if it was some kind of a joke at the Koch brothers' expense.

1. https://translate.google.com/#de/en/koch

I believe that's how their name, Koch, is pronounced and not any sort of literary device.