I haven't seen a better suggestion than Sync for a block chain 2.0 network. We can use either Sync or BitSync.
If the BS abbreviation might have negative connotation, perhaps consider SyncBits?
Network is Sync, which has Bits in there i.e SyncBits. And then later if there are apps like chat or anonymous web or markets or whatever, they could be SyncChat, SyncWeb, SyncMarkets etc. Or pegged assets like SyncDollars.