I pretty much always nickname my pokemon since it makes me feel closer to my adorable little pixel friends as I send them into battle with my special names for them. A lot of the time I'll just name them since I'm bored, though. My mood usually affects the naming process, which doesn't work out so well if, say, it takes me a really long time to catch a particularly stubborn pokemon and I've gotten angry at it, because then sometimes I end up naming it something kind of mean... but then I go back and get it changed later, of course (well... usually). I like the names of those in my main team the most, since I try to make those very fitting, and even if some are kind of silly, I get attached to them. :>
Also, I had no idea that you couldn't rename traded pokemon....