So far it has been theater on the inside and now its going outside.. Hence the name i suggest would be

1. Amphitheater - the Amphitheater series...
or
2. Colosseum - Best known amphitheare
3. Flavia - the dynasty that built the Colosseum

I strongly lean towards the Amphitheater series because it is intuitive and can be the label for a whole series of them....