I generally don't rename characters except in single play games where you generally control the same character for the entire game and are given some degree of flexibility in creating that character (i.e. Mass Effect, Dragon Age, Kingdoms of Amalur, Pokémon etc) Beyond that I just use the default names the game provides. Even in Zelda games I always call Link, Link.

I think the only real exception to this is XCOM where I named everyone after colleagues, friends and forum goers.