Change Apple ID name

Log into your account and in the first section, click edit. That will allow you to change the name associated with the account. You can't remove/change @iCloud.com, @me.com or @mac.com aliases. You can create a new alias if you want to use it for iCloud email.

Apple ID - Manage    

iCloud - Create or change email aliases.   

See the instructions below.

Change your Apple ID (Be very aware of the restrictions here.) https://support.apple.com/en-us/HT202667

Before changing your Apple ID using a computer, sign out of all Apple  services that use your Apple ID. If you are going to use an iPhone, iPad, or iPod, then stay signed in with your Apple ID on only that device. This instruction is taken from the above documentunder the heading Before you change your Apple ID.

For sign out purposes, see Where can I use my Apple ID? https://support.apple.com/en-us/HT202659 “This list is provided for informational purposes only and is subject to change without notice. It's not intended to include every feature or service that uses Apple ID. Visit the Apple ID support page for more information.”

There may be some redundancy, but see What to do after you change your Apple ID or password 

 https://support.apple.com/en-us/HT204071