I understand why it's called a bank because it does provide lending services and deposits do earn interest; however, my experience when discussing it with others is that calling it a bank is a turn off because A) semantics and B) most people don't like banks.
Even though the Federal Reserve is a disgusting entity, they were smart to recognize the negative connotations associated with the word 'bank' and intentionally left it out of their name to gain public trust. I think BitsharesX could just as easily call itself just an eXchange OR an "Exchange Cooperative".
In fact, I think "Bitshares Exchange Co-op" not only sheds a more positive light but it could be argued that it's more accurate as well since 'co-op' means an autonomous association of people (or business) that operates through consensus for mutual social, economic, and cutural benefit. Given that, if someone approached me asking if I wanted to join their bank I'd decline immediately.. whereas if they asked me to join their co-op I'd consider it.