I gather that the problem is with the @icloud.com address, not the Apple ID itself.
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, which require a different Apple ID).
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