I have what sounds like the same issue with Mesh. But my setup is just one computer that is syncing with the online folder. When I contacted MS support about it, here is the response I got:
If Windows Live Mesh detects multiple versions of the same file, both versions of the file will be saved in the folder. The files will be renamed, appending the computer and user name of the person who created or changed the file. To consolidate the files, you must merge the versions by opening each of the files and consolidating the information.
I replied that multiple versions should only occur when there are multiples machines sycning to the same online folder (like your situation). They agreed, and want me to do some tests to determine the cause in my single computer setup.
But for your situation, is it possible that the files in question are changing on two of the computers, and that is the reason for the duplicates, which would then be by design? And are you still seeing the original file, in addition to the one with your computer name appended in the file name?