Has anyone tried to use the laser to engrave the label of a DVD disc ?
The best solution might be to apply spray paint over the label layer and laser that off, since a lot of those label layers are reflective (I’ve seen non-metallic label layers on some blank CDs, but never on DVDs that I can recall). Keeping the paint off the disk edges could be accomplished with a (laser-cut!) cardstock or paper cover that masks off the last cm or so. The primary risk with lasering the things at all is that you might damage the foil data layer, so you’d have to do some careful tuning.
If you intend to do more than a couple of these, though, you’re better off seeing if you can find a LightScribe drive and appropriate media (both are uncommon now, but still available), since that’s a purpose-built solution that’s guaranteed to work.