Move to other screen keyboard shortcut

YES, there is a way - at least if the screen keeps the same name.

You may notice that is just about any Mac application there is a "Window" menu, and in there you will see "Move to ..." commands, where the name of the display(s) is/are shown.

For example, I have a Samsung display "SMBX2431" and also an iPad as additional displays for my mac.

Since the current window is in the built-in display, this is what I see in the Window menu:

You may have noticed that I also have a Keyboard Shortcut assigned: Command-Option-Control-LeftArrow.

And it works, too!

All that I had to do was adding the shortcut in System Settings->Keyboard->Shortcuts->App Shortcuts:

This is not possible with any macOS shortcuts. You could use a third party app that enables these shortcuts. One app like this is called Swish. Just note that Apple is not the developer of these apps and cannot offer support for them and they could potentially cause issues. (This app has worked fine for me so far)

semouk wrote:

My main concern, that screen are not keeping the same name. So every time I'm attaching new display I should go through this annoying process again.

Not if you regularly connect to the same displays. You can set shortcuts for them and they will still be there the next time. You can (probably) even assign the same shortcut: for example, say you have a display "A" at home and a display "B" at work; you can assign the same shortcut to "Move to A" and "Move to B" as they are not going to exist at the same time. No need to do anything further.

Of course this does not work when you attach a completely new display, but how often are you going to do this?

There may be a way to capture the name of the displays and programatically create the shortcuts, but I am afraid that the work to figure this out is likely to outweigh the benefits.