The serial number label for desks, credenzas, and returns is placed on the outside kneespace side of the top drawer. You will need to fully extend the drawer to find it.
If you have difficulty locating the label, fully open the top drawer and “clap” your hands on the drawer sides. The serial number label should be under or near your hand on the kneespace side of the unit. If you have a double pedestal desk, check both the right and the left drawer for the label.