I just use Windows to rename, copy, backup, etc.

Me too, just use the OS rename functions.     Seems like a misuse of programming power, so no, I don't vote for this one. 

As some other posters mentioned, if you rename the cwp and the project folder, that should do the trick. One thing of note is that the audio files within the project folder would still have the old project name as the prefix of the .wav file names.
 
Within the project, sometimes if you click on Track -> Copy track names to clip names (which would change the clip names) and saving it afterwards would sometimes update the wav file names. Most of the time it doesn't help though.
 

When I do this, I do a Save As, with the copy all audio option checked, and in the Save As dialog box I create a new project folder with the new name and make sure I navigate to the new project folder before completing the Save As.
 
This copies all the ACTIVE audio clips, (just the ones still in use in the project), with the new project name, into a properly named project folder with the new name.
 
Does the above what you seek to achieve?  I am able to do it entirely from within the Save As dialog box AND trim old clips in the process. And hitting ALT+F, then A, launches the Save As dialog.
 
Bob Bone
 

For me at least,  part of the idea behind my request was to simplify the process and not leave unused folders laying around in the system, and make sure all folders follow the old project. I understand that these functions are part of the way Windows handles any program save as or rename. There are  work arounds some of which are great ideas  I intend to try...so maybe this is moot and seen as a kind of redundancy. Some of these ideas involve a physical renaming of folders and re direct. This is what I'm trying to avoid.
 
What I seem to end up with when I save as under a different name are two projects.
 
In using a "save as" with copy all audio checked everything is changed to the new name, but are there still files left from my older creation under the old name? If so this seems to be a waste of HDD space IMHO. Essentially we have created two projects.
 
Maybe I'm making something really simple harder....if so I have digressed. I mean, it isn't really complicated to do it the ways stated, but if it can be made into a more direct process with less chance of user error and save disc space why not?

Studio One does it easily (just File -> Rename). This automatically changes the name of the project's folder, project file in it, and the project in the Recent Files list both on the startup page and in File -> Recent Files. The list of course does not contain the pre-renaming project, since it no longer exists. 

I don't happen to feel any particular burden at the fact that a Save As with copy all audio leaving the original folder out there.  All I then do is a single click on the old folder, and hit SHIFT+Delete and it's gone - permanently, not moved to the recycle bin.  So, for me, the total duration a 2nd folder is out there is a matter of literally a few seconds.
 
While anything that does help streamline tasks and time is generally a good idea (meaning I am certainly not opposed to them doing something like what you seek, it's more of a 'when' thing for me) - I would myself vote that their developers address other more helpful changes, like to Step Sequencer dealing with eighth-note meter bases, or nested folders, or track colors being saved with track templates.
 
Bob Bone
 

This may only to apply to a few people who are chaotic and bad at planning :) BUUuuut.  
 
I would like a simple way to rename project folders and project files.  Very often I start a project with no idea of what it will be about or what it should be titled.  Thus I create the project named after a synth voice or instrument, or "Loud and Boomy."  Then I work on it a bit, figure out a title, and set it aside for working on it later.
 
Later, I remember the actual real title I gave it, but not the project folder's name.  So I go thru project folders opening sessions till I find the right one.  
 
I would love it if I could press "Edit -> Project -> Rename Project" and get a dialogue to rename it.  The the original project folder could be given a new name, files moved to it, and the original stupidly-named project folder would be deleted.

Not a bad idea.  In the mean time, I use Save As for a work around
 
I do the same with initial names of yymmdd_UNP
 
Then I use Save As when they shape up a bit into something real.  The added benefit is that the initial start is still there if I want it for something in the future

An earlier thread on the same subject:
http://forum.cakewalk.com/Allow-Renaming-of-Projects-m3195569.aspx
[Link now redundant due to threads being merged]