You may need to access the files for your iPhone/iPad/iPod Touch backups on your computer in order to delete or rename them.
Each backup of a device is typically named by the unique device identifier (UDID). You can find your device's UDID by clicking on the Serial Number field in iTunes (which will switch it to your device identifier.) Some folders will have a date/time stamp after the UDID as well.
On a Mac your backups are in
/Users/your username/Library/Application Support/MobileSync/Backup.
- Open Finder, and select the “Go” menu at the top of the screen. Hold the Option key, and select the “Library” menu option from the Go menu. (On OSX Lion and above, Library will only appear with the Option key held.)
- From Library, navigate to Application Support -> MobileSync -> Backup.
On Windows, your backups are stored in
*your user account data folder*\Application Data\Apple Computer\MobileSync\Backup. The user account data location varies for different versions and configurations of Windows.
- Windows 8 and 10: In the Windows search bar type %appdata% (with the percents) and press return/enter. A file browser window will open to the Application Data folder.
- Windows 7, Vista, XP: From the start menu, select Run. In the run box, type %appdata% (with the percents) and press return/enter. A file browser window will open to the Application Data folder.
- From there, navigate to Apple Computer -> MobileSync -> Backup.
I'd be remiss if I didn't say: Make sure you know what you're doing before you muck around in your iTunes backups :)