Here is the only way I was able to solve this problem. As a freelance editor, my jobs require that my Reviewer name be anonymous. I had to create a New User and login using that name in order for it to show up as the alternate reviewer name. My machine is currently running OS 10.9.5, Mavericks.
1. Go to System Preferences
2. Go to Users and Groups
3. Bottom left, click on "Click the lock to make changes." It will ask for your password.
4. The left panel is now accessible.
5. Under the "Login Options" click on the "+" to add a user account.
6. When adding the new account, I made it an "Administrator" account using the first tab in the new window.
7. You can then name the account (name desired for your Reviewer comments), add password.
8. Log out as current user and login with alternate account. The name of the new account will show up as the Reviewer name.
The only downside is that you need to create everything anew, as far as I can tell, as this new account is a new, independent user. Therefore, I had to email the docs to myself, then using the new account login to my email, download the docs, and go. If anyone can find an easier path, I would appreciate it. As many others have noted, simply changing the name in Word did not solve the problem.