Yes Ian is pronounced EE-an as you suggest (as is its variant Iain unless you are being very picky about pronounciation).

One of the greats of English cricket of the 1980s was Ian Botham and during a test match between England and India (or Pakistan)... Let me digress for a moment: on the BBC Radio commentary it is the usual practice to have at least one of the commentators from the opposing team's country. Right, got that? Okay, I'll continue... and one of the commentators from the Sub-Continent continually pronounced his name thus (to much hilarity amongst the listening public)

I-An Bot-Ham

but factor in his accent and it often sounded like:

Iron Bottom