Network Time Machine problem - OSX Update renamed computer?

[randy98mtu]

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.

[Gugulino]

I would say that when you choose the renamed backup volume in Time Machine preference panel, Time Machine will recognize your backup and is not going to start from scratch.

[randy98mtu]

Originally Posted by Gugulino

I would say that when you choose the renamed backup volume in Time Machine preference panel, Time Machine will recognize your backup and is not going to start from scratch.

Thanks. I'll give it a shot tonight.