Spaces: Rename Desktops
It is possible to rename spaces using an app called Spaces Renamer. It is available on GitHub for free.

  
  The compressed view after pressing F3


  
  The expanded view after hovering


  
  The interface for renaming the spaces

Image sources: the GitHub page
Please note that to use it you have to disable System Integrity Protection to use this tool. You'll need to download MacForge to use it. All of the installation instructions are on the GitHub page.
It does not work for the time being on macOS macOS Big Sur due to increased system protections there. Only time will tell if it will be supported there. However, it works perfectly fine on macOS Catalina.