I don't know about FFIX specifically, but the established convention for characters with multiple names is to use the name that the character identifies with (except for dialogue, of course). So if she thinks of herself as Garnet, she's Garnet, and if she thinks of herself as Dagger, she's Dagger, no matter what anyone else is calling her. The only exception might be Zidane's chapters, if you're dead set on third person limited, and from a stylistic standpoint it might be useful to indicate the switch more clearly. Don't you think?