I want to change my Apple ID Name....it is misspelled. Not the email address, just the name.

See the instructions below for changing an Apple ID.

Change your Apple ID  https://support.apple.com/en-us/HT202667Read these two sections very carefully to see what is allowed: If your Apple ID is a third-party email address and How to change your Apple ID if it ends with @icloud.com, @me.com, or @mac.com.

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 document under 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.”

And see What to do after you change your Apple ID or password 

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

To change your name, log into your Apple ID, and in the first section, click Edit. That should allow you to change your name.

Apple ID - Manage