I think you should go with a name that's not so much a pun, and obvious parallels with existing services:
Bitcoin Stock Exchange (BCSE or BSE)
Or something easy to remember:
Bitsto.com (for 'bit stock' and currently avaliable)
BSE, isn't that the officia term for mad cow disease?
Bisto is a brand of gravy in the UK & Ireland, so Bitsto is a little too close for comfort.