I think no, for several reasons:
"BitShares" refers to a bunch of different DACs, not just the exchange
"BTS X" refers to a family of bank&exchange DACs (each with finite number of BitAssets), if the first one is "BTS" then what do we call the others?
XT will be used as a snapshot target (100% of at least first X chain will be direct XT snapshot) and won't be upgraded to any X chains (that's the plan for now at least)
Eventually we will need a hierarchal naming scheme no matter what