I was confused by this at first, because Insta doesn't have my real name on it anywhere, and it's not linked to my (now lying dead and unused) Facebook account at all. But if you mean no anonymity because of phone numbers, that is true. I did need to give my number to get my account, but I guess I never considered giving my phone number as part of giving up anonymity (though I guess it does mean they can track me down if they want to for some reason).
It's a fake-ass name on my account, though, as well as a fake-ass birthday, which is all I really ask for.