In the 7th Singularity, Fou-kun is referred to as a "Beast of Calamity" (災厄の獣, saiyaku no kemono) by Ishtar / Ereshkigal. Obviously, this may be a generic designation for all Beasts.
Tiamat is referred to by Merlin as a "Beast of Original Sin" (原罪の獣, genzai no kemono). This too may be a generic designation.
Tiamat is referred to by Gilgamesh as "the Beast of the Beginning" (原初の獣, gensho no kemono).
In LB5-2, Koyanskaya is referred to as "a Beast of Black Fog" (黒霧の獣, kurogiri no kemono). (This I'm not sure on?)