This sounds like something is broken and should not normally happen. Please make sure you have the latest version 1.71 of CloudMe Sync installed on all your devices. It is really important in order to avoid conflicts.
If one of your computers are constantly creating these conflicts, then please exit the CloudMe client in the taskbar, then uninstall the entire application (to reset the local database), then reinstall the application and login using the same username. This will unfortunately require you to specify yet another new computer name, but the database will be rebuilt and the conflict problems should end.
Please email us if you continue to get this problem and we will help you investigate further.