The procedure to change the name is below, but you have to be able to sign into the ID to change it, which requires your password.
Contact Apple ID Support for assistance recovering the password. See the Apple Support articles below for contact information.
Apple ID - Official Apple Support.
Contact Apple for help with Apple ID account security - Apple Support. (Link doesn’t always load)
Get Support Work through the screens to get a chat option. You may have to pick a slightly different problem.
Apple Support schedule phone call
https://twitter.com/AppleSupport. People have posted it may take an hour or more to get a response.
From the Apple Support article below.
Without proof of your identity via security questions and other carefully selected criteria, Apple Support can't help you reset a password or perform any other actions on your account. These policies are audited and reviewed on a regular basis.
Security and your Apple ID - Apple Support.
Note the restrictions in the article.
Apple ID Name Change.
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.