I normally name myself my real name, but in Platinum I wanted to be a girl for a change, so named myself after my Niece. Thinking of doing the same again, or maybe some random girls name.
My Rival will be called whatever pops into my head when I'm making him, can't remember what he was called before LG, but in LG he was Bob, Dave in Diamond and Black (Going by names of colours here, even if black is a shade not a colour).
My Pokemon get called whatever random name I can think of when I catch them, I tend to go for something random, I have a Snorlax named Gaz (Yes that's a COD referance xD).