We all believe that it is a title of honor. I don't really buy in to that.
Naming Blair "Heart of the Tiger" would be like calling Thrakhath (or rather more fittingly, Melek) "Head of the Ape" (..or-whatever-simian-like-creature-you-guys-have-on-Kilrah). I understood it the same way as Toast, but more as a somewhat cryptic and cumbersome tactical designation for the most dangerous pilot of the Tiger's Claw. The Hobbes-trigger fits well into that, apart from the inconsistencies LOAF mentioned.
But there's more, thinking along that way: "Tiger's Claw" must have made Kilrathi either groan in disbelief or snigger in contempt - the name is so presumptious. It is as weird as if one of the kat ships would have been christened "Tooth of the Gorilla" (..or-whatever-simian.. etc.).
When I was playing the game in my teens, I liked the name, but later it made me squirm each time. It reeks of military pathos and things not really thought through. Why insult an enemy even more by making allusions to an almost-extinct earth animal? Why choose an identity that makes yourself a component of the analog image of your enemy (talk about mixed metaphor here)? Doesn't it sound wussy to call a warship "pincer of a yellow cat", if you were a Kilrathi?
So "Heart of the Tiger" from the mouth of a creature for which a tiger must be an inappropriate and inferior caricature of itself would be at least a well-placed quip, if not an underhanded and deadly insult.