He/Him
I think Nolan was hesitant to use any character that they wouldn't be able to do anything with them in the long run or name a character that would get tarnished by a writing choice. A couple examples assumed by fans being Anna Ramirez who could have been Renee Montoya, a couple chances at Harvey Bullock and then Juno Temple playing "Jen" who is completely Holly Robinson from the comics. It also could be because of paying creators of the characters too.It's extremely weird and frustrating considering I feel like - and my perspective may be skewed but I don't think so - the Bat-family as a whole are pretty popular. Like, I know Batman & Robin flopped terribly but did it really scare filmmakers off from using any characters outside of Bruce that badly? It's crazy to me. The fact that Two-Face kidnaps Gordon's wife and son and Barbara - a long-established character who is his daughter - isn't there or even mentioned is extremely irritating to me. And having her be there would have been perfect set-up for her to be Batgirl in Dark Knight Rises. An extremely missed opportunity. I hope there is a Robin introduced in The Batman sequel like has been rumored. I think it'd be really interesting to see.
And that's definitely part of it for me too. The first live-action movie about a non-Batman member of the Batfamily was so exciting, especially since Barbara is low-key my favorite member of the team besides Bruce himself. I am genuinely devastated it was so unceremoniously canceled and will never forgive Warner Brothers.