Is there a way to change the name of my Network?

Is there a way to change the name of my Network, or is it always going to be [my name]’s Network? For example, I’d like to have a network for my family and a separate network for my work colleagues and maybe a third network for a group of friends or my sports team, etc. I understand this might be somewhat accomplished by creating a separate Project for each group of people but I may also like to have multiple Projects subsumed under a particular group of people. I suppose that can be jimmied with Labels, but I don’t think that was its intended purpose.