There's two types of sumerian tablet
those made by writing
those made by cylinder seal
the cylinder seal ones are genuinely referred to by their catalogue number and location
Hence the one that Sitchen made famous is Va 243 berlin. Many copies may be made but there is only ever one original seal

Now and then a new version of an already known story will emerge from the silt
So they are known by the period they are from
e.g. Anything in its original sumerian format is known as standard,
the rest are categorised by the period they are from
so you can read Gilgamesh (standard) or Gilgamesh (old babylonian)

As for the rest, receipts and citation forms they are normally categorised by location found and date. These ones tend not to get rushed to the translators all that quickly and as such the whole world has currently missed the fact that Enlil is Enki's father and not his brother

But as John says
It depends on who is doing the categorisation
all the good stuff is here already
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