"She did not remember her name."
Translation:Hon mindes inte vad hon hette.
Sound good. That would be more consistent. To give some context, in another multiple choice question, the translation was for something like "He forgot everything", but there was an another option available for "He remembered nothing" (these probably weren't the exact options, but they were along these lines). I selected both choices and was marked wrong as one wasn't the correct literal translation, even though it was semantically the same. With this question, I'm not marked wrong for not selecting options that are semantically the same. I find I'm learning which answers to press, and not what the answers actually mean in these cases.
Vad heter du is what are you called/named, I think you should add that as a separate Enlish translation and if in multiple choice translations someone only picks "what's her name" for the sentence with the same literal meaning you should accept it. I do know what "vad heter du" (wie heißt du/hogy hívnak), but I don't think its literal translation is widely used in English, it might be unfamiliar to native English speakers.
It would change the meaning. When she is the subject of the sentence, her own things must be referred to with sin/sitt, if you say hennes it can't be her own. So there's no room for ambiguity in Swedish here. (This refers to the possible translation Hon mindes inte sitt namn, not the main translation above which is constructed differently).