MOST IMPORTANTLY, do not check the 'Comments, Revisions, Version, and Annotations box' - checking that box can lead to the deletion of all comments in the document.
The author of your comments will change to 'Author.' If this does not work, close the document and reopen it. Note that these instructions will not catch identifying information in the text of the document itself (for instance if an author has included their name and title at the beginning or end of the manuscript, in an acknowledgments section, etc.) Word for Mac 2016/Office 365 Here are instructions for anonymizing comments, tracked changes and file 'Properties' in a Word document.