Question: will eevee evolve on its own sword?
Answer: You can catch an Eevee on Route 4 in Pokemon Sword and Shield. It's very rare, but sometimes you'll see it in the overworld! Be aware, the Gigantamax gift Eevee you get for having Let's Go Eevee saved data will not evolve! If you want a Hidden Ability Eevee, you will have to catch one during a rare Max Raid Battle.