Possible meaning of Begrazia
>Be + Grazia (Italian for Elegant) or "Be Elegant"
>Be + Grazia/Gratiae or a reference to the Graces, a trio of Roman Goddesses. They were also called the Charites which is Grazia in Roman
>Grazia is also Thank you.

I particularly like this as it parallels Re;Iris' naming. Both the goddess allusion and the "Xe" + Word convention. A future unit would then be called Le:Parcae or something.