I would say it's a little of both, but I'll also throw in the whole "Everyone (but you) knew Yda was Lyse the whole time" thing, as to me that's a clear enough symptom of the problem. First impressions are important for establishing who a character is, and my first impression of "Yda is really Lyse" was that all of the characters who should be surprised by this already knew, and just kept me/my character in the dark because it didn't matter if I knew or not. Yda would still be Yda, no matter what name they called her by.

And from what I remember of Stormblood's story, that much is true. They didn't do anything with Lyse that they couldn't have done with Yda, and didn't change her character in any particular way to differentiate her from Yda—aside from taking away her dynamic with Papalymo and giving her nothing in return. So in a roundabout fashion, changing her identity actually made her less interesting.