HT4895: Using your Apple ID for Apple servicesLearn about Using your Apple ID for Apple services
If the ID doesn't end with @mac.com, @me.com or @icloud.com, you can rename it by following this article: http://support.apple.com/kb/HT5621.
After renaming the ID, go to Settings>iCloud, tap Delete Account, then sign back in with the renamed ID. This deletes the account and your iCloud data from your device but not from iCloud. Provided you are signing back into the same account, your data will reappear when you sign back in.
If you are also syncing you Mac with your iCloud account, you'll need to go to System Preferences>iCloud, sign out, then sign back in with the renamed ID.