It should have other markings, though probably not words as such. It might have a date, and a code marking on the receiver ring, maybe a code stamp or trademark on the toggle. Also, note that Lugers were made in two calibers, one being the now common "9mm Luger" and the other the "7.65mm Luger" or ".30 Luger" with a necked down case. The latter should not be confused with the 7.65mm Browning, which we call the .32 ACP.
When recording military Luger serial numbers, make sure to record the year of manufacture, the manufacturer, and the letter suffix below the serial number on the front of the grip frame. The reason is that serial numbers often started over each year, each maker had his own series, and the letter suffix is part of the number.
So all three elements are necessary for a positive identification; any one or even any two will not uniquely identify the pistol. If yours is a police lab, failing to do this could let a smart defense attorney wrap you up and hang you out to dry.