I think your name should relate to whatever the focus of you network is. For instance, MySpace is designed to give people their own "space" on the web where they can put their favorite pictures, favorite music, and a few thoughts. Facebook is designed to simply connect people with all the other people whose faces they recognize. So what is your network going to focus on?
This brings up the good question of what type of network isn't already covered by the big 2? Realistically, unless you have a really good answer to that question, then your network will never take off the ground. So find a purpose first, and then we can suggest a creative and catchy name that fits.
