It is possible to rename spaces using an app called Spaces Renamer. It is available on GitHub for free. I am unsure if it can change the "default" name of desktops as you requested, but it can customize the name of desktops you already have. Please check the below screenshots for an example.
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.
A different way to "name" or "identify" different desktops is by changing their wallpapers, as desktops can have individual wallpapers. However, this unfortunately will not be helpful if you have applications and windows that are covering the whole screen area.