privaTX feels a bit awkward (to both write and pronounce) and is similar enough to InstantX that it might cause some confusion. Personally, I'm fine with Darksend, but if we're throwing ideas out there, how about something simple like "SafeGuard".
for average users, it might be better to just use the word "Send", and then you have 2 pots of coins, public and private, and you choose which pot to send from. You could move coins betwen the 2 pots (moving coins to the private pot anonimizes them, moving back to public just sends to yourself). Might be a dumb idea, just thinking about average users might get stuck with all the options / 'Darksend' / coin control and how to abstract that.