How do I delete an Apple ID?
Delete Apple ID from your iOS devices
Now you need to remove your Apple ID from all of your iOS devices. You’ll need to follow these steps for each Apple iOS device (iPad, iPhone, and iPod touch) using your Apple ID:

Tap Settings.

Open iCloud.

Tap Delete Account.

Open iTunes &amp; App Store.

Tap the Apple ID and Sign Out.

Click Music.

Click your Apple ID under Home Sharing and tap Sign out.

Tap Mail, Contacts, Calendars and Sign Out.

Open a Message in settings tap Send and Receive.

Tap Apple ID and Sign Out.

Tap Game Centre, choose Apple ID and Sign Out.

Tap FaceTime and Apple ID and Sign Out.

How to get Apple to delete your account
The answer seems to be that you currently can’t get Apple to delete your accounts (or at least there is no permanent and automated way to do this.

What you can do, however, is edit your personal information to make it a little less personal. Once you’ve removed your Apple ID from all your devices you can change your name, address and other personal details

Follow these steps to change your Apple ID information:
Visit https://appleid.apple.com.

Click Manage your Apple ID.

Enter your name and tap Sign In.

Tap Edit next to your name.

Change your name and tap Save.

Tap Addresses in the sidebar to the left.

Tap Edit, change your address and tap Save.

Tap Phone Number, enter a new area code and number and tap Save.

Tap Sign Out in the top right corner.

You should now have removed your Apple ID from all your devices, and changed all of your permanent information. That Apple ID is now toasted. Remember that you won’t be able to access or use any purchases or apps connected to that Apple ID without authorizing it on your devices again.

source: macworld.co.uk