There was a Jeopardy question last night or the night before about Batwoman. Nobody answered correctly. One guy rang in and said "batgirl" but Alex denied him.
That's the other part of the issue with this show: she's hardly some beloved character. A Batgirl show would've been a much better choice because even if you went with a Barbara Gordon or Cassandra Cain version, both those have fans. Nobody cares about Kate Kane. Her hype was a decade and a half ago when she was the highest profile LBGTQ character at DC, but that's old news now. She never brought much to the table beyond that.
In fact, now I've made myself sad that we didn't get a Cassandra Cain Batgirl show. That could've been awesome. Of course, the CW would've just made it about who she was dating and added a generically attractive supporting cast of bland characters, so it doesn't matter.