I just want to make clear that my timer suggestion was just as last resource alternative. I'm all for an event when someone puts on or takes of a mask.
And the reason I suggested renaming the mask itself was both for being realistic and easy to implement. If you see someone with a mask and latter another person with the same mask, you'll easilly think it's the same person. As for implementation, it would be fairly easy to set dynamic naming for masks, I guess!
Anyway, I like WojD's idea of not renaming the mask. You see the person put on the mask if you're present, you'll see "a person with a cotton mask" do the actions, but you won't be abble to tell one from another. This will make thiefs life a bit more easy without breaking game balance. The only drawback with this one is that it won't be possible to exist masked heros since you won't be able to identify them. What do you think is more important? I guess there won't be heros anyway, so I vote for not renaming the mask.