Once you have created an iCloud account and chosen an @icloud.com address to go with it you can't change the address (short of creating an entirely new account). If you have both an @me.com and @icloud.com address (with the same text before the '@') you cannot delete one of them. If your @icloud.com address is also your Apple ID and login you cannot change it to a non-Apple address.
However, all is not lost. You can add up to three 'email aliases' - these are additional addresses (not accounts) which deliver into the same inbox as the main account. (In fact it's a good idea to give out alias addresses, rather than the main address, because if they attract spam you can easily change them.)
You should be aware before you start that once you've created an alias you cannot turn that address into a full iCloud account or move it to another account.
More information on aliases here: https://help.apple.com/icloud/#mm6b1a490a