How do I permanently delete my Apple ID?

See this document - Understand and control the personal information that you store with Apple - Apple Support and use the links in it.

With recent changes (May, 2018) to Apple’s privacy policy, you can either temporarily suspend an AppleID or permanently delete it. Note that deleting it also deletes all data associated with it - iCloud data, purchases, everything.

Visit privacy.apple.com to make a request.

You can't delete an Apple ID. All you can do is log out and stop using it.