Was it all just a nightmare? - From the character's point of view, something could be a nightmare.
The reality is bleaker then usual. - What the character's thought was a nightmare was the truth.
I was burnt once then restored, - Two places match this: Nibelheim and Correl.
Now you might have never guessed it. - A person/character not native to the place would not suspect anything.
What is my name? - Nibelheim, the reason being was that the Shinra company rebuilt Nibelheim so well that no one would have expected it's nightmarish past.

As Choco got that first - I'll let him take the floor if he wants to.