It is possible to rename spaces using an app called Spaces Renamer. It’s available on GitHub for free.
The compressed view after pressing F3
The extended view after hovering
The interface for renaming the spaces
Image sources: The GitHub page
Note that to use it, you must disable system integrity protection to use this tool. You need to download MacForge to use it. All installation instructions are on the GitHub page.
It currently does not work on macOS macOS Big Sur due to increased system protection there. Only time will tell if it is supported there. However, it works just fine on macOS Catalina.