We do this often at my organization. I'm attaching instructions I put together for our editors. Note that the context is slightly different: our editors are usually selectively changing several authors to the same author name, not just changing one.
The instructions are simplified a bit -- you don't actually have to extract all of the files. But I wanted the process to be simple for our editors, and this method ensures that all "stories" (body, headers, footers, etc.) in the file are searched. It also handles issues (author initials showing) that can crop up in PDF'd versions with track changes shown, plus a somewhat recently added people.xml file that can cause issues with identifying authors whose names you're trying to change.
Finally, you can save several steps by using
7-Zip (free, widely used), with which you can directly extract XML files from Word docs -- no need to add a .ZIP extension -- by using the "Extract to" feature, which creates a folder with the same name as the Word file. Next, follow the attached instructions, beginning with step 6.