The name makes sense, I agree, but it just doesn't sound marketable to me. It sounds boring.
I think it's too bland and confusing for the average joe, who's only just able to wrap his head around Bitcoin. 'Shares' sounds even less like 'money' to newcomers, and face it, we're still at the stage where 'digital money' is what most people crypto think is. I think I read somewhere that HyperLedger or somesuch name is proposed, and I think that's a better idea for the DEX itself.

The shares part I would ignore completely in terms of marketing.. just move that to the back-end group of users who are versed enough in the platform to participate in that part. I see it more as an extra feature rather than the main thing that needs to be promoted. The strongest point Bitshares has, IMO, is the fact it's a DEX, and I think it should focus on that primarily.