If the character isn't visually customizable I use the default name. If they are, I make them look like me, then I either use my real name if it's appropriate or Eirikr, the most ancient form of my name, if it's a fantasy game where using my real name would clash with the lore. (Sometimes in Japanese games I use Erikku just to be a weeb.) I like to put myself in the game when possible so it feels more like I'm really there. I don't see the point in attaching my name to a preset character that clearly isn't me though, because that would break the immersion.
If I get to name my rival, I name him Gaylord.