I live in Ireland and would say it Ee-va. Just like the name Eva. Never ever heard it said Av-va or whatever that other Irish person said but then again it could be a different dialect. Names like Aoife and Aoibheann all start with an EE sound as do all the words that start with Aoi in the Irish language itself which I speak fluently. I quite like Aoibhe.
It's NOT pronounced AY-va! AY-va would be spelled as Éabha.