Euan is said you-an and
Keir is said Keer in Scotland and they're both Scottish names! I've never, ever met somebody who says them at all differently from that. Maybe they are pronounced differently elsewhere in the world, but here in Scotland we pronounce them both the way you like.
However, ee-mon is way too like demon and RYE-s is 'rice' to me. Not a great name really (although there was a girl called Rice in a Beethoven movie).