Coh-burn is the normal here for this surname (and “Cockburn’s Port,” which made an advertising point out of it)
It’s near-impossible, for me at least, to pronounce it that way. It’s the other ‘ch’ sound, the one farther back in the throat. The one that you start “Chanukah” with.
A few months ago, I met someone with that name who pronounces it Kaw.
I heard Sam Koch’s (of the Baltimore Ravens) name mentioned on TV today and it was pronounced cook.
When you say “kaw” is that different from “kah” to you?
If it’s the Billionaire family, I’ve always thought it was pronounce “Coke”- and it bothered me when people (who should know how to pronounce it) would always refer to them as the “Kochtopuss.”
Yes, of course, because I’m from Maryland, which, like most of the East Coast, does not merge the “cot” and "caught"vowel sounds. If you are a native of New Hampshire, you’re from one of the few areas in the east that does merge them. Or you’re originally from somewhere out West.
Koch means cook in German, therefore those Kochs who pronounce their name “cook” choose to preserve the meaning of their name rather than the pronunciation.
Nope, I pronounce them the right way (different from each other). I was just checking which you were. 
A slightly different example is Henry Bloch, founder of H&R Block. He pronounces his own name like the company name, and he spelled the company name that way because most people pronounced his name as “Blotch.”
On a related note, I went to grade school with two sisters whose last name was spelled Cocke and they pronounced it “coke”. Later in middle school we got a new student who also spelled her name that way. The teachers would mispronounce it as “coke” and the girl would yell out "it’s COCK!
Very informative–to summarize:
–Ends in hard “k”:
Coke
Cock
Cook
–Ends in soft “ch” “sh” or “ah”:
Cotch
Coach
Cosh
Kah, Kaw
–German:
" …which is like “ko[kh]” with the [kh] representing an “h” like sound, like the “h” in “loch.” "
Again, “Kah” and “Kaw” represent two different pronunciations.
And somewhere out there, there’s probably someone who pronounces it “Throat Warbler Mangrove.”
If you want to be precise, in IPA the pronunciation is /kɔχ/. Or you can listen to native pronunciations here.
In college I knew someone who pronounced it Coaf (rhymes with loaf).
Bill Koch, younger brother to the infamous Charles and twin the infamous David, very definitely pronounced it “Coke.”