The name bitnet.cash
from the marketing point of view
sounds better is more catchy although it looks like is only related to digital currency and digital payment system.

As you said you would build the whole ecosystem i mean not only payment system the name opensha.re  suits better
for the purpose

(Open shared reward economy)

so is really difficult choice to make.

bitnet. short, simple and to the point. instantly recognizable.

openshare has nothing to suggest blockchain tech. sounds like an openoffice module.