As an Englishman I am puzzled as to why some American men I heard pronounce the name Missouri as 'Missoura'. Did I mishear? If not, why so?

No, you did not mishear. I live on the Plains, and it is frequently used here, even by friends who live in Missouri.
Probably a variant of the "southern" accent on so many things.

It's a regional thing. It depends on what part of the state you're from. The radio show A Prairie Home Companion was in St. Louis some time ago and they asked the mayor of St. Louis how the state's name was pronounced. He responded quite confidently with one pronunciation or another (I don't remember which). A little later in the show the governor of the state was on and he pronounced it the other way.

I might wonder why you, as an old Brit, would wonder about this, considering the fact that you have three towns named Hough fairly close to each other with three completely different ways of pronouncing the name.

'Missoura'

I'll ask Chomondely Featherstonehaugh, next time I see him.

and both the Amayrican and the Amurrken will tell you that they don't have an accent - but the other feller does.

Chomondely Featherstonehaugh

I'd like to meet him.

I had a Native American grandmother, whose name was Featherstone.

Probably true in most locales: towns and other landmarks pronounced one way by the locals, and very differently by others. This
becomes very obvious when a local TV station, say, hires a new
weather forecaster who talks about the temperatures in the
neighboring "tri-state" area and pronounces these places like an
"outsider" would.

Chomondely Featherstonehaugh

In case some might not know the "proper" pronunciation of these two names, it's Chumley Fanshaw.

Yes, that makes sense. ( featherstone ) (wetdesert)

Thank you Faldage. I didn't know there are three Houghs in the UK. Can you tell me please how they are pronounced?
Google says there are several Houghs in the US:
Hough, Mississippi, MO 63834, US
Hough, Carroll, AR 72638, US
Hough, Texas, OK 73942, US
Hough, Adkins, Bexar, TX 78101, US
Hough, Augusta, Woodruff, AR 72006, US
Hough, Vancouver, Clark, WA, US.

I'd be interested to know how (Hough?) they are pronounced.
By the way, it's Cholmondeley not Chomondeley.
On the subject of pronunciation I used to cringe when I heard George W. Bush say "Isreal" for "Israel". Could the man not read?

There's a lot of city names in the US that are in widely separated states. I believe the pronunciations of the various Houghs in the UK are huff, hoe, and how. Perhaps some knowledgeable brit can correct me.

Isreal is a fairly common pronunciation of Israel in the US. It's a word that probably most of us hear before we can read and it sticks with many folk. Of course, a truly correct pronunciation would be something like YEES rah ell, but that's a little bit farther than most would go. The common 'correct' pronunciation in English would be something like IZ ray ell but the sort of things that happens to unaccented vowels tends to drive them towards the GWB pronunciation.

Interesting todays citizens call themselves Israeli,
whereas Scripture refers to them as Israelites.