No problem. Typically a large manufacturer like Dell will have Windows utilities that allow you to see the service tag of a monitor through software, if that's possible. Just as they do for the PC's service tag, either using the BIOS or software like ours.
I performed a quick search for such software from Dell, but couldn't find anything. As far as we know, the only unique value that can be pulled from monitors through software is the serial number. It's possible Dell could add this to monitors, but we haven't seen it yet.