The good thing about cats is that they come in various sizes of litters. If it was one cat each time, you'd have no basis for the naming system, but when it's a litter of six, well, there aren't many choices:
Six simple machines (Good names, I must say.)
Six regular convex polychora (This is what I used. They can be long, though.)
The Big Six (I should re-read those books sometime.)
You can't name a litter of six cats Alpha, Beta, Delta, Tux, Tumbleweed, and Velcro, after all. They need to be consistent.
Similarly, if there's a small kitten named Qilin who vanishes, and later a very similar one is born to the same mother, but you're sure it's not the same one because it should be older by now, right? you can't just name it 'Bob'. It has to be Sabitun Sabintu.
So that's what I did. Shame everyone else refuses to call him that.