Depends on how much influence the game has on the character. In games like Mass Effect and Dragon Age where you pretty much decide everything about who the character is, like their gender, appearance, personality, background ect, giving the character a title or a nickname usually works best.
If however it's a game where the character already has a set gender, personality, background and stuff, then it's fine to give the character a name. The Witcher and Walking Dead are good examples of this. You get to make the decisions, but the character's still the same person.