Dave,
And after thinking about the best way to describe CB's Connections, the best analogy is Facebook Friends. It's not exactly the same but very, very similar.
Now, if you want to change the name of it from Connections to Friends or perhaps Networking then you'll need to indulge in a bit of hocus pocus with some more 3rd party Joomla extensions. Initially I'd leave it as is until you feel it's functionality serves your purposes on your test site before trying anything else. If you then feel you want to change names then post back here and I'll explain how I did it.
Nick Coe
www.k9sportworld.com
www.ellmoregroup.com