I'm for Mythic Monsters. Lots of monsters are from myths or lore, so 'mythic' fits, but mystic implies magical, and not all monsters are magical in nature.
Oh, oh! You play the game on a phone, right? And that phone can fit in your pocket when you're not using it, so it's like the monsters are in
your pocket! POCKET MONSTERS! Genius name idea; you can't go wrong with this one! +10 points for me.