I came up with a whole set of eevees, and I've got art for all of them. I'll post them here later, but for now, here are the names.
*Created by Nintendo.
+ My translation of a nintendo Jap. Name.
Bug - Mosqueon - The name comes from "Mosquito".
Dark - Umbreon* - I'm guessing that the name comes from "umbra" which means darkness in Latin.
Dragon- Majesteon - Comes from "Majestic", which I always thought the dragon types were.
Electric - Jolteon* - Comes from the phraze "Jolt of Lightning"
Fight - Athenion - Comes from "Athena" the Roman Goddess of war.
Fire - Flareon* - Comes from Flare.
Flying - Aereon - Comes from "Aerial" meaning "In the air".
Ghost - Spookreon - Comes from Spook. I was always scared of
Grass - Leafeon+ - My translation of "Leafia".
Ground - Minreon - Comes from Mineral.
Ice - Glaceon+ - My translation of "Glacia".
Normal - Eevee - If Eevee does hit every type, I have a feeling that there will be no new normal type.
Poison - Acideon - Comes from "Acid"
Psychic - Espeon* - I'm guessing that this is from E.S.P, which is used to describe psychic powers.
Rock - Stoneon - Comes from Stone.
Steel - Ironeon - Comes from Iron.
Water - Vaporeon* - Comes from "Vapour".