OK, yeah, makes sense that the New World would have another name that has nothing to do with its relation to Eorzea, makes sense that she would visit it, no further questions there.

"I've spent a lot of time in the Thirteenth recently! There was a guy there who kidnapped one of Bahamut's brood, so I was helping her brother get her back!"

There's. A whole lot more to the story than that, but apparently this is what she feels is the most important part.