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Each institution has there own cataloguing system. In addition to that the archaeologist, if any, will have their own identification system which is usually dig-specific. So, for example, items dug up one season might have a different coding than those dug up the previous season. It all depends on the archaeologist.
Ideally you would give all the numbers you had. So, for example, if the artifact has an archaeological coding and a museum coding, you would give both.
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That kerbstone is simply called Newgrange K52, since it is the 52nd kerbstone at site Newgrange K, counting clockwise from the entrance.
An example of the use is in the Cambridge Archaeological Journal in an article covering many other sites.
I doubt there is a systematic classification which provides an answer for something which does not yet have a name.