MacBook Air 13'

Looks like you're using your Apple ID across your iOS and macOS devices. When I do the same all I ever see is the last 5 digits of the serial number depending which device I'm viewing my other devices on.

In the picture you've shown you can see you've a very poor Wi-Fi signal. Move as close as you can to your Wi-Fi access point and refresh the screen. Perhaps you'll now see the same?

I'm not sure of how the information gets there in the first place? I think its related to your Apple ID and possibly ties in with purchases you've made from Apple? Hopefully someone may post who knows more than I do about these things?

Good luck!

You don't. It's already there. Click on the Apple Menu in the top left hand corner of the screen and select "About This Mac". Do you see it?