According to Charles D. Roberts, writing in The Kindred of the Wild, he gives a little history of the fable. He says of the (unnamed) tiger:
These earliest observers of animal life were compelled by the necessities of the case to observe truly, if not deeply. Pitting their wits against those of their four-foot rivals, they had to know their antagonists, and respect them, in order to overcome them. But it was only the most salient characteristics of each species that concerned the practical observer. It was simple to remember that the tiger was cruel, the fox cunning, the wolf rapacious.
He mentions several by name (Reynard the Fox, Isengrim the Wolf, etc), but does not name the tiger. I've not been able to find a name for the tiger in my research either, though, that doesn't mean there isn't one. Just that I've not found it!