There are 3 approaches to renaming presented here:
manually renaming/editing
use a 3rd party tool
leverage a project template
I've not used either of the 3rd party tools to accomplish renaming so cannot speak to relative pros & cons and in particular their ability to handle multi-project solutions.
I have used both the manual and template approaches and the determining factor in deciding which approach to use is the complexity of the layout in VS
manual renaming will retain open windows and files
using a project template the work space needs to be recreated
Both of these approaches retain References and project files.
I initially avoided the template approach because it appeared to be unnecessarily complex but it is actually much easier (and safer).
The manual approaches are amply addressed here but the template approach needed a bit of research the results of which are presented below.
[Instigated by @Edoardo ().]
Using VS2022
While in the Solution select Project->Export Template which launches a wizard. You'll need to decide what to call the template -- this will be the title displayed when creating a new project -- and where to save the template. The default save location is %USERPROFILE%\Documents\Visual Studio 2022\Templates\ProjectTemplates. I use the default.
VS handles selecting essential project elements and copying them into a zip file with the same name as the template. Copy the template name into Notepad or whatever you use.
Exit and restart VS.
Select Create a New Project. Initially your new template is not a displayed option.
Paste the template name into the Search bar at the top and VS adds that as an option.
After the projject is created clicking on References shows a warning icon for all NuGet references. Right-click on the poject and select Manage NuGet Packages. When that opens click the Restore button in the warning message at the top. This will install all of the missing packages.
Build the Solution.
The result is a duplicate of the original project with a new name, correct .sln & .csproj file references, clean output bins and correct Namespace, project properties & assembly info.
NOTE: performed with a single project solution. Based on the using statements at the top of .cs files I assume nothing more is needed for a multi-project solution but that is unconfirmed.