- When I look at my note 10 I see a screen with clock, always on display. What is the name of this"screen"?
It is commonly known as Always on Display. It is a feature commonly found in devices with AMOLED display. See its wiki page for more information on this.
- If I double tap on this screen, I get another screen that tells me to swipe to unlock. What is the name of this screen?
- When I swipe, I get the login screen. This is simply called the login screen?
It is recognized and called as the login screen. Developer oriented manuals however might not use this term. For example, the screen where you (the user) are required to authenticate yourself using PIN/password/pattern/biometric might be called as login prompt. But everyone understands it as login screen and the term is acceptable to both general users and power users of Android.
- Now I'm logged in and I'm on the home screen? Main screen. Start screen?;)
It depends. If your device went to sleep (display turned off, either manually by the user using power button or because of screen timeout) and the user was using an app other than launcher app, the first screen you would see after unlocking the device is that last app you were using. Otherwise, if you press Home button / home gesture, than the screen you get is one of many Home screens. Home screens are part of a home launcher app. A home launcher app is one such app which manages your home screens, the contents displayed on them (such as your app and web shortcuts, app widgets, etc.), and also allows the user to access the installed apps using another screen called app launcher.