When we were in Eyam this weekend, we were debating whether it’s pronounced Eee-am or I-am. Fortunately, we checked on-line before trying either of these words on the locals, as it’s pronounced Eeem. This is what The Concise Oxford Dictionary Of English Placenames has to say about the origins of the village name:
Eyam, Derbyshire. Aiune in Domesday Book, Eyum in 1236. From Old English egum, the plural of eg, or island.
The origins of the word are likely that Eyam was an island area in between moors or marsh, with the word island in Old English being ‘īeg’.