When I go to my Microsoft account it shows 1 serial number for my Surface Book. Serial number are used just like MAC addesses to identify specific devices. The Surface Book is sold and manufactured as 1 item with 1 serial number.
The serial number for your Surface Book is on the bottom edge of the Clipboard where it attaches to the keyboard.
If you can’t read the serial number on the Clipboard, you can use the serial number on the bottom of your keyboard. Registering this serial number will automatically register the serial number on your Clipboard.
To find the serial number for your keyboard, turn the keyboard over and look for the number on the bottom next to the rubber foot.
I am not disputing this but there ARE two serial numbers. Unless they changed something in the past few months. If you go into the settings on the tablet, you will see that the serial number for the clipboard is different than the serial number etched onto the bottom of the base. Look at your box too. There are two serial numbers on it as well. One for the base and one for the clipboard. Again, unless you received a unit recently and they changed something. Both the unit I purchased in Jan and the unit a friend purchased in June have TWO serial numbers. They sold and manufactured with TWO serial numbers. Although I think that for warranty purposes only the base is registered, which is why you only see one online