copy the whole project folder and give it the name you want
you cannot rename the project file or any of the project members(schematics, pcb, etc). If you open the project file in the renamed folder, all referenced project members have identical names as the originals, but are the copied ones in the new folder
There is an option to archive a project (in the project manager: File > Archive, or use the toolbar icon), which creates a zip of all relevant project files. You could use this, but copying the files in the folder to a new folder like you said pretty much does the same thing and skips the zip and unzip steps.
I know that this is an old topic, but it came up at the top of my search. I was wanting to take an existing project of mine, and make a new project out of it. The new project is going to have many similarities, and it would be the quickest way to get started on the new project. I don’t really want the project and file names to be the same as the old project. It takes a little work, but overall I don’t think that it was too bad.
My project has several sheets. Fortunately for me, all my sheets began with the same name… like “BVS_01_MPU.sch”, “BVS_01_Memory.sch” and “BVS_01_IO.sch”. I used Notepad ++, Find in Files to search for “BVS_01” and replace it with the new name I wanted. This took care of all the references inside the files. Next I used a utility call “Bulk Rename Utility” by TGRMN Software to rename all the file names from “BVS_01” to the new name.
That was it. I opened the project and everything had the new names and opened fine. I hope this helps someone else out.