When documents are shared to be editable by "anyone with the link," they should still be able to comment in their name if signed in
It seems that it the only way for you to know who are the persons who are editing or adding comments in your Word document is by changing the sharing option. This is unsuable for document collaborations.
ideally this would function as google docs does: Anyone with the link can access and edit; if you sign in, comments you make appear with your name attached to them. if that's not how this works, I will unfortunately have to go back to google docs. sigh