I'd like a native or advanced speaker to confirm, but my understanding is that the word order given in this sentence is preferred in a negative statement like this, where the emphasis is simply on not being something. The full sentence you're comparing this to was "Én nem Éva vagyok, hanem Kati", where there are two contrasting statements, and the emphasis is on who the person is and isn't.
In English, the following sentence doesn't necessarily have any particularly strong stress:
"I'm not English" ("Én nem vagyok angol")
But if we have two contrasting statements, there'd be a slightly stronger stress on the two words being contrasted (in this case those indicating nationality):
"I'm not English, but (rather) Hungarian" ("Én nem angol vagyok, hanem magyar")
In Hungarian, the corresponding words will also have a stress, but the word order changes more often to emphasize something, and the words being emphasized typically will move closer toward the front of the sentence.