Android - most top bar name?

That is called the Status Bar. You can set the color by overriding your Apps style theme with:

android:statusBarColor="yourColor"

Let me know if you need help setting up the style correctly.

This region is called the Notifications area. https://www.tutorialspoint.com/android/android_notifications.htm

UPDATE It's actually called Status Bar while the expanded section is called Notification Area.

Some websites (see above) incorrectly call this Notification Area, and they call the resulting expanded section Notification Drawer