"his Beauty, his girl-child, his pet"

By giving the heroine of this tale the name of 'Beauty', Carter asks us to recall the original European of 'La Belle et la Bête', or 'Beauty and the Beast'.  The first known written version of the tale appeared in 1740, by Gabrielle-Suzanne Barbot de Villeneuve, and has since been retold through every artistic medium.  The girl 'Beauty' is not just physically attractive; she is deemed to be gentle, kind hearted and innocent, which (seemingly) sets her in opposition to the Beast.