I honestly think the best description of what bitshares "is", would be "blockchain". DAC works too, but from what i understand then DAC is synonymous with blockchain. There are plenty of established english words that work well as metaphors for describing and simplifying what bitshares is; company, community, cooperative etc. But all these words are just approximations, and I dont think we will ever be able to find an established word that properly defines bitshares, because nothing even remotely like bitshares existed before bitcoin.
So given that satoshi decided to name his invention "the blockchain", we might as well use that name too (if DAC causes confusion due to the company part)