I actually prefer the Pokémon I receive in trades to be nicknamed. I, myself, nickname ALL my Pokémon. Not because I want to leave my mark or anything, but because it's easier to tell the difference between my Pokémon that way.
If I had 10 Clefairies and was going to trade a few of them away because they didn't get the right nature or whatever, it's much more easier for me to think: "So Barbie, Venus and Cookie have Magic Guard as their ability? Might as well, put them up for trading"