I have setup my iCloud account linked to an old email address on my iPhone 5 whit iOS 7 installed. Everything works great except iCloud. I obviously forget the old password and want to change it to the new email address. However, iOS 7 promptes me for my password but displayes the old email. It’s crazy that I need to enter the password to delete the iCloud account and also can’t change the iCloud username ID.
By default once you’ve setted up your iPhone, tap Settings > iCloud, tap “Delete Account”, then sign back in with the new ID.
The account and your iCloud data will be removed from your device, without from iCloud.
However, to delete the existing old account from iOS 7, you need to type the password, if you don’t know it, you’d better contacts Apple support and ask them what you’re supposed to do.