if there's already a default name there but they let you change it, i'll stick with the default name even if it sucks. it helps me immerse into the story and with the game outside of the game, because everyone refers to the character as the default name.
Depends on the games. More often than not, I'll leave the default name if there is one (Tidus in FFX comes to mind).
If I'm given the option of completely naming a character, I usually go with Elge. Sometimes if I can pick a first and last name, I go with Samuel Dalaran (the Persona 3 and 4 games allow this).
I don't change RPG names, like Star Ocean, or Final Fantasy. Especially if they speak the names. But if it's something like Pokemon, I will change it. [Usually Cambria, and the rival is Coheed. Or in Platinum when I'm Upah and my rival's name is Omar. Lmfao.]