How do I change my email address (APPLE ID) to match my new name

You can change your Apple ID email address on your current Apple ID so you retain access to your data and prior purchases. Note the restrictions in the article.

Apple ID Name Change.  * 

Make sure you turn off Find My Phone before signing out of the old ID. Once signed out and Find My Phone is off, then sign in with the new ID, then turn Find My Phone back on.

 What to do after you change your Apple ID or password - Apple Support  *  I suggest doing this before you change your Apple ID or password.

You have to use the iCloud address that is associated with your current Apple ID .If you create a a new iCloud address, you are creating a new Apple ID, and you will lose access to all your current data and purchases.

Based on what I have read, I suggest you leave your Apple ID email address as a 3rd party email address because you have more flexibility if you need to change the email address. For example, if the Apple ID got compromised, you can change it to another address. I also have read of many people who were locked out of their accounts when they forgot their password. Since the recovery email address is the @iCloud email address, if you forget your password, you also can't access your email to get emails from Apple to recover your account. You can set a rescue email address, but for some people, this hasn't worked.

You are welcome. Use any email address you have that isn't associated with your current Apple ID email address. If necessary, go to AOL or Yahoo and create a new email address.