You don't need to add the impurites, they're already there. Metals have fairly distinct patterns of impurities depending on where they were mined from and it's basically impossible to entirely remove them. If you expose a sample of metal to a large flux of neutrons (usually in a reactor) then the nuclei of the various elements in the metal will absorb neutrons and then decay. The products of these decays can then be analyzed to work out the composition of the metal even if an impurity is very small. This type of analysis has been common for a very long time now. An example of a current use is determining the country of origin for controlled metals like plutonium and uranium.
There are ways to get around this kind of approach (by adding impurities, not removing them) but I felt like mentioning it because it makes a lot more sense in this context than isotope fingerprinting.
