You can only change your ID to the @me.com or @icloud.com versions of the address, which will still have the same text before the '@'. The only way you can change the main address is to get a completely new Apple ID,, which will cause you a lot of problems.
However, though you can't change the login (which no-one else sees) you can change the email address you give to people. 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