Yes, if you choose Eevee in Round One, for Round Two you can evolve it into anything you want. Before Round Three, you can change that Pokemon's moveset, ability, etc. But it has to stay as that Pokemon.
To be clear, just in case:
Round One = Eevee
Round Two = Umbreon
Round Three = Umbreon with edited movesets, ability, etc, if you so choose.
Please remember to provide your Pokemon Showdown username in your post!