traveller Mac can be used without an account, you can install apps outside the store. But in iphone/ipads without logging in you cant really install any apps.
traveller If one doesn't use real name when creating Apple ID?
Even if you dont use real name, when you keep your sim card it will link to the mail id and can identify your name if you have an old account, if its new one they will have other ways to find your real name like credit cards or wallet. More over we dont know what are the data they collect about us.
If you are concerned about privacy dont use iphone, if you want a secure device with some privacy issues go ahead. But we already have something thats secure and private so that should be the first option, and second is iphone of course.