You can change your Apple ID name by following these instructions:
you can manage your Apple ID from AppleID.Apple.com, this is the only place you can make permanent changes to your Apple ID and iCloud account names, password, etc.
Hope this helps
also for FAQ about Apple ID: support.apple.com/kb/he37
Oh and if you mean that these changes are not taking effect on you iPhone after using appleid.apple.com to make the changes, then do this:
In order for the changes you made on to your Apple ID / iCloud account thru appleid.apple.com to take effect on your iOS device (if it doesnt happen immediately), you need to delete the account from your iOS device first (basically logging out), then add it back using your updated details. (Settings > iCloud, scroll down and hit "Delete Account", then settings>iCloud, sign in)
Providing you are simply updating your existing details and not changing to another account, when you delete your account, all the data that is synced with iCloud will also be deleted from the device (but not from iCloud), but will be synced back to your device when you login again.