OK, here's the story on Mac OS X
As written in my other reply on Windows vs. OSX, I explained that OSX has the capability to detect renames or moves on disk based on a file's (and folder's) unique File ID.
And programs written in Cocoa, using the document based classes to manage opening and saving files represented in their own windows, this should all work unless the programmer screwed it up. And even Carbon apps get this right if they're written properly (i.e. following Apple's guidelines):
Apple actively wants every app to support that the user can, while a file is opened in an app, rename or move that file (on the same disk, i.e. volume), and the app should learn of the change and keep referencing that same file. A good example of this is that, on OSX, you can also rename a folder containing your file, and it should not cause problems (on Windows, it usually does!).
So, to answer your question: You can usually rename a file you're working on, only that this isn't working the way you like it to: Apple has never suggested to add a Rename command, and instead suggests to either (or both) offer a "Save As..." and/or a "Save A Copy As..." in place of your preferred "Rename", resulting in more freedom: Not only can you rename but also move the file to save this way. Adding another "Rename" would only lead to confusion, if you think more about it.
Plus, you can rename and move the file on disk in Finder, if the app is written properly.