In Pokemon Black/White, can the Name Rater remove a nickname?

I had a Patrat that I taught Cut, but once I got Strength I taught another Pokemon both Cut and Strength. Now the Patrat is redundant. But when I came across the Name Rater I renamed Patrat to +Cut. (I named the other pokemon +CutStr.) Earlier today I found the Move Deleter. I used him to delete Cut from +Cut. Then I flew back to the Name Rater and tried to remove the nickname from +Cut. I tried entering a blank name, but the result of that was that the name was unchanged. Then I tried naming it Patrat, which worked.

Has its nickname been removed, or do I now have a Patrat whose nickname is Patrat? What would happen if it evolved? Would its name become Watchog or would it evolve into Watchog but still be called Patrat? (If I had enough Rare Candies then I would try it out to see what happens, without saving the game, but I have only 4 Rare Candies so far.)

In Gen4 and Gen5, there's no distinction between an unnamed Pokémon and one nicknamed its species name. This differs from Gen3, which had a "nicknamed" flag. A Pokémon loses its nickname when it evolves, if its nickname is the same as its species name in any language.

In one case, I had a Japanese Vibrava (named ビブラーバ, its species name). I had to evolve it to Flygon to fill a gap in my Pokédex, but I didn't want to because I knew it'd lose the nickname. In the end, though, I decided to let Flygons be Flygons.