The same happened to me last year. It wasn’t as bad as your case where they got your details. In my case the scammers just kept trying to get replacement orders sent to their address for computer parts totalling £700 I’d ordered a few weeks ago. I have no idea how they managed to impersonate me.
The most frustrating thing is how Amazon customer services refuses to believe there is an issue and just keeps telling you to reset your password. EVERY TIME.