I've been thinking a lot about the idea of the City being built up after a great fire and the more I think about it the more I really like the idea. I get these pictures in my head of a towering inferno with a classic caped wearing, maniacally cackling super villain at the heart of it, some big name villain of the past who (supposedly) died in the blaze he started.
Depending upon how long ago the fire occurred this also allows for there to be very distinct areas of the city which aren't 'reclaimed' yet and which are essentially slums or derelict sections only partially rebuilt by companies looking for cheap land to industrialise close to the city. These areas might not have the best mobile reception and therefore be extra dangerous as the medical signals that call Totally-Not-Docwagon are less likely to work, and yet may not be all that distant from vibrant, thriving areas of the city.
Emergence is a good name choice. Just as a second option with roughly the same meaning, perhaps 'Advent' City?