To use the screen reader, ensure that you've enabled VoiceOver (macOS).
Select System Preferences > Accessibility.
Select VoiceOver > Enable VoiceOver > Open VoiceOver Utility.
Select Navigation and select Move VoiceOver cursor from the Mouse pointer dropdown.
Start Illustrator and open the New Document window. The VoiceOver cursor will be able to focus on the elements and announce their names.
When you press the keyboard shortcut to invoke the tool, the VoiceOver Utility announces its name. It also announces the name of the artboard when you access it in Presentation Mode (Shift + F).