You partner Eevee name: Satchel the Eevee (Can I have a eeveution from the start?? Or do I have to evolve it by getting points?? If so then I want my Eevee to be a Umbreon named Satchel.)
Why do you like Eevee?: Eevee are cute and I like the fact they can evolve into many different Pokemon of many different types. My favorite being Umbreon.
Anwer the Current Topic: Eevee as a starter? I can see that seeing that Eevee's Blue's starter in Pokemon Yellow and Eevee is the starter in Pokemon Conquest. Though there would need to be a way to access the evolution stones and Moss/Ice Rocks early on.
Edit: Eevee is also the starter for Pokemon XD.
No you have to evolve your Eevee by earning points.