Strange Time Machine problem

I've done some searching and haven't found this problem listed anywhere. I have an external drive on which I put my Time Machine backups. Somehow the backups.backupdb folder now has two folders "Myname iMac" and "Myname iMac 2." In the second are my most recent backups, and when I manually start a backup it goes into the second, but when I open Time Machine from the Dock, or from Applications, it opens the first folder and doesn't see the most recent backup. I tried moving the items in the second to the first, but it won't let me move backups. None of the items are duplicated in the folders so combining them should just result in a complete history of my Time Machine backups.

So, any bright ideas on how to combine these two folders and have a true history of my backups? Or even how to get to the most recent backup instead of the folder of old backups that isn't being updated?