I had to do this for my mom's Kindle app, although mine was done when it was still available to do on the amazon page. It is not on the amazon page now and you have to do it on the app. The name was whatever I had named my iphone and my mom's iphone. Then it showed up under the "Registered Kindle Reading Apps". I don't remember, but I think I then changed the "Send-to-Kindle E-mail Address" on the "Personal Document Settings" page. Now she can read whatever is in my library or whatever I send to her that was converted.
Registering the Kindle App
To register your Kindle app, use your existing Amazon account e-mail address and password. If you live outside the United States and use the Kindle application, please see the Using the Kindle App if You Live Outside the United States Help page.
Logging into your Amazon.com account through the Kindle app registers your device to your Amazon.com account. Once you sign in during registration, you won't need to do it again -- just open the app to access your Kindle Library.
Tap the Kindle icon on your iPad, iPhone or iPod touch to open the reading app.
Enter your Amazon.com account e-mail address and password.
Tap the "Register" button.
You can also tap the Settings icon (the cog) on the Kindle Home screen to view or change your account registration.
Signing Out and Deregistering
If you sign out of the Kindle app, your reading app is deregistered from your Amazon.com account. When you deregister, you can't download content to the Kindle app or send purchases to the app unless you register again.