Probably only way to stay anonymous - if your hardware wallet is delivered on parcel machine (don't know how exactly it's called in English). Your name isn't needed there, phone number or email is enough. You'll get PIN code through SMS or email and this code is needed to open doors of that parcel machine.
Amazon run Amazon Lockers in a number of cities, and you only need a code which they will email you to pick up a package. A new account not linked to your real name or address and a throw-away email address could be a possibility, although knowing Amazon, they will lock your account at the first sign of any shenanigans.
Unless the hackers used fake IDs when registering the phone numbers (which they probably did), the carriers could help in identifying the users behind those numbers.
I'm no expert on the matter, but it used to be that simply phoning your carrier and saying that it is business phone and you would like it to be registered under the name of your business (in this case "Ledger") would be sufficient. It's even easier if they are using a VoIP service, with many letting you simply fill in the field yourself. No ID required.