It is a griffon, a beast of fantasy. Part lion, part eagle, all nobility.

[Gilgamesh sets Nobu down upon its back, a weight the animal endures easily. As if a proud parent, it begins marching about with its little rider, beak tipped high and wings shifting to accommodate. If she looks close, she will notice they are slightly bent and broken—this griffon was injured, but you wouldn't know it from its happy demeanor.]

His name is Dinoriel. If you treat him well, he will be good to you in return.

[Is Gilgamesh undertaking the taunting task of trying to teach Nobu manners? It would seem so.]