My post-fix comment:
There's just one problem with this that I've discovered since I had to redo our docs in the move from vB to XF... you can't abbreviate Conversations to anything. With Private Messages or Private Conversations, it's easy enough... but if you've only got Conversations, you're stuck having to spell the whole long word out every time, or come up with Conversation Messages just to abbreviate it to CM, but then you make up unofficial terms again so you might as well use PC.
The added downside to having Conversations only is that you can't use it as a verb (whereas "PM me/him/her" or "PC me" works fine), so you have to spell out the entire "start a conversation with..." every... single... time... which gets tedious really, really, fast.
So I'd argue in favour of changing this to whatever has two words purely for practical reasons. We all know how many hundreds if not thousands of times we've written "PM me" and the like over the years. You'll regret having to write "start a conversation with me" instead every time VERY quickly.
Dropping the "Private" (or Personal) bit also very easily creates confusion with all the users not used to the XF terminology, as already mentioned above.