If the game gives a name to a specific story character (and not a crappy one), I stick with the default. (i.e. Cloud, Chrono, Issac), but if I need to give a name and.or if the character is supposed to be "me", I go by Striker.
As far as online, my main online alias Jonathon Striker, and I'll use full name, Striker for short if forced, or even J.Striker because Striker is common in some games. I also have sub aliases: Mr. Pink, and BlackM4G3 (blackmage). Mr Pink is for anytime I can use the Hot Pink, or Black and Hot Pink color theme, and then my friends and I joke about "hiding in plain sight". Black Mage is whenever I play a Mage or wizard class, and I say I'm Black Mage because I'm black. That actually started with Xbox 360 Bomberman Live, and then Ragnarok Odyssey because I made myself a dark-skinned Mage with an Afro.
HighScores are always my Alias Jonathon Striker, or just Striker, unless restricted to initials, and then I use mine: JEC.