Network Time Machine problem - OSX Update renamed computer?

My MBP has been having a hard time backing up the last 2 nights. Tonight I looked into it a bit more to figure out why it kept saying it couldn't locate my backup drive. I had it mounted on my desktop. So I looked at the "select disc" and I think I see the problem. I don't know how to change it or how it happened. It says my backup is on "My Book on "Randy's Mac mini"". Under Available discs, it shows "My Book on "Randys-Mac-mini"". So the difference is obvious, but I didn't change the name of that computer. Is this a change in the latest OSX update? Do I need to delete my old backup and let it do it all over again? Rebooting made no difference and my wife's computer is having a hard time even logging in to the Mac mini. Any help would be appreciated.

Edit: I just realized I didn't describe my setup. I have an AEBS running the show. The Mac mini is hooked up by gigabit. The laptops are WiFi. The backup drive (a USB3 MyBook) is plugged into the Mini.