Well, the current logo does say "bitshares"...and lowercase is considered hip, modern, and cool...and many people are lazy and apparently don't like to capitalize when typing, so I'm sure "bitshares" will often be typed either way...so I'd just say match the logo and keep everything simple: "bitshares".
Don't mix the things, look to other logos for example new balance, yes at the logo all letters is lower case and now look to the site and over Internet, yes - it's New Balance.
Now, let's see how this will look in the wiki for example:
"Bitshares is based on the bitshares toolkit, which gives it many inherent advantages. Bitshares has Transfer Invisibly To Any Name (TITAN) and Delegated Proof of Stake (DPOS) in addition to several other novel features." - do you like it? I'm not!
Bytemaster blog:
"Stable bitassets by bitshares Video"?