At least the light novels are giving us a drama CD, with it being about an original story written by the author. Who knows one drama CD can lead to more things, possibly?
You should understand that it indeed means "white tiger" but in Japan it is also the name/term of one of the 4 divine beasts from Asian mythology.
Well, the Japanese were pretty "original" using that name but it still is the name of the divine Beast.
@Talh
yes I fully aware about that, but if we're talking about this series then Byakko is her epithet, Byakutei is her title, and Kohaku is her name. You even can see the kanji for Kohaku (琥珀) that Touya wrote on the ground.
Also there is no peculiarity about "white tiger" either, that's basically just how Japanese people say white tiger in Japanese and at the same time, the mythical beast is a tiger with white fur. So if an English speaking people addresses this beast, it will be "the white tiger".