Console games I tend to just use the default name. If there is no name available, "Chaos" is my typical standby.
In the case of online games, Chaos gets taken within the first five minutes of a game going live, so I tend to be a little more unique. If the game has a considerable amount of lore behind it, and I know at least some of said lore beforehand, I'll try to make a name that's at least semi-lore-friendly.
Otherwise, I'll simply use referential; I'm particularly fond of the Japanese language, even though I can barely speak three sentences worth, so whenever I make a new character or name a new pet I'll pop up a Japanese Dictionary and look up words for a good half hour or so.