No, you can't rename traded Pokémon legitimately, you will have to use a cheating device for it such as an Action Replay.
Here is the Action Replay code for it.
5215BE54 2800FB2B
0215BE58 B0022001
0215BE5C 1C388028
D0000000 00000000
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There is a name rater in Castelia city.
Needs to be traded from Pokemon White.
Unfortunately, you cannot nickname traded Pokemon in this game, or any Pokemon game for that matter. You can nickname your own caught Pokemon by going to the Condominiums next to the PokeMart in Eterna City and ask the old man near the entrance. I hope that you will make do!
You can rename a pokemon by going to the Name rater
Eevee cannot be found in pokemon black or white, and must be traded to be obtained.