No!

[That would be him. Not... any of them.]

[Damian takes a moment to phrase it... in a way that he imagines that might be understandable.]

Superhero - vigilante - identities usually are a second personality of somebody who has a - a life that is registered and subjected to the laws. There are names, and addresses, and day jobs, or school for the younger ones. In that way, both Batman and Batgirl are identities. The identity of Batgirl is modeled after Batman's. The person wearing the mask - or cape, or whatever - is not affected by those choices. Not on a biological level.

Other than the scars, of course.