You might want to check the name of your phone by going to Settings>General>About>Name to be sure it's still the same. If it isn't, you can change it to the name you want there, but I don't think that's the problem you are having with iTunes.
To fix this, assuming you have a PC rather than a Mac, uninstall iTunes and all of it's components, then reinstall iTunes by following the steps in the guide: http://support.apple.com/kb/HT1923. Be sure to follow it exactly, removing each of the components in the order specified. )This will only uninstall the application, it won't touch your iTunes library or data.) Then try backing up to your computer again as outlined in my earlier post.