In the release of macOS Catalina, Screen Recording is new a PPPC prompt that requires any application that shares the user's desktop to have the end-user approve the access.

Only 1 user on a machine needs to approve the Screen Recording PPPC prompt. Once approved by any user of the machine, it applies to all users of the machine. The prompt only needs to be accepted 1 time. The approving user does not need to have Admin rights. 

When connecting to a device, you will see not see the desktop. You will only see:

Below is a tutorial on how to guide the end-user to allow the Screen Recording prompt.

  1. The end-user will be prompted to Open System Preferences and navigate to Screen Recording to approve the application:
  2. The end-user will need to click the enable option for this application:

If the end-user doesn't enable this option, you will not be allowed to view the end-users screen.