I rarely get .doc files, so compatibility mode isn't the problem. But in Word 2016, every .docx file arrives in "Protected" mode and I have to click "Enable editing". After that, my tracked changes correctly show my initials, except in certain documents.
In answer to your other post, yes, the first link https://www.razumny.no/2017/05/word-track-changes-shows-up-as-author-instead-of-author-name/ includes clear step-by-step instructions on how to fix this 'Remove personal information' setting.
My only problem is that it doesn't apply retroactively, so my current document still shows all my existing tracked changes and comments from yesterday as "Author", but new changes and comments today get my initials instead.