I have not worked with Word for the Mac for many years. Is there a Ctrl-F6 or Command-F6 keyboard shortcut? This would cycle to the next document. The same with the Shift key cycles to the previous document.

In Windows I have my taskbar displayed on the right side of the screen where the individual document names can display.

You might want to explore this question on a forum dedicated to Word on the Mac.
http://answers.microsoft.com/en-us/mac/forum/macword