Apart from Iranians and nearby countries, the BBC probably gets it right the most, although they can go overboard when pronouncing Chinese and Hispanic names. As far as I've heard, only Americans, and maybe some Canadians, but less so, refer to it and Iraq, as Eye-ran and Eye -raq.
This causes much mirth in England and Europe and furthers cultural stereotypes, much as Bush used to say "nucular", when the word "nuclear" has no way logically to be pronounced like that.
OTOH they really don't care what others think since it works for them and they don't need to talk to people who have different ways of talking, at least usually. So the situation becomes eye-relevant and they don't become eye-rascible, although if challenged, they may legitimately become irate i.e. Eye-rate.
BTW: In Iran do they call our county Amer-eye-ca?
(when it's not the Great Satin that is? Dunno what a fancy cloth has to do with Satan though...)