How do I change the Apple ID without the old password

"If you forgot your Apple ID password" click here --> https://support.apple.com/HT201487

What to do after [or even better, before] you change your Apple ID email address or password - https://support.apple.com/HT204071

If you still need help:

Contact Apple for help with Apple ID account security "This article provides country-specific Apple Support contact information for customers seeking help with their Apple ID password or other security-related issues."

https://support.apple.com/HT204169

or

Contact Apple for support and service - "See a list of Apple phone numbers around the world." - https://support.apple.com/HT201232