Android - What is the offical name of the third on-screen button?

It's called Overview button. I originally came to know about this from the Screen Pinning settings' description.

Google on Get around on your device (see Get around with navigation buttons) has noted:

Overview: Opens a list of thumbnail images of apps and Chrome tabs you’ve worked with recently. To open an app, touch it. To remove a thumbnail from the list, swipe it left or right.

• It looks like this

  

• If your device is running Android 4.4 or lower, your Overview button looks like this

  

This is called 'Recents' - you can see info about it here

EDIT

As Dan Dascalescu points out, it's now called "Overview".