Her maiden name was Heartilly. If she changed her name when she married General Caraway, it would obviously be Caraway. The game doesn't tell us this in any direct way but she is usually called Julia Heartilly when her name does make the occasional appearance.

Now, there's no way that could be wrong. So I'll just keep this thing going:

When does Quistis give you the tutorial on Status-Atk Junctioning?