And while the second half of that term can easily be transliterated as both 'Liger' and 'Ryger' or several other minor variations thereupon, The Author Hath Spoken.

Besides, it's not like it's supposed to actually be the one from the show; if it were then the show's preferred transliteration would be correct. But it's not, this is UF, so Gryph gets to be picky and have his choice of what sounds right when he tells the story.

If anyone has a right to be picky about the name, it's Kozue, and you don't see her complaining, do you?