User blog comment:TheDoctor230/The Multiple Arrow Identities/@comment-7890302-20170219153418/@comment-3221148-20170223194225

That's only in DCAU. I think Prime Earth Gordon knows that Bruce is Batman, IIRC he was all "finally you remembered" when Bruce got his memory back and showed up to stop Mr. Bloom last year.

Though Gordon had to suspect something when Batgirl stopped appearing exactly at the same time his daughter got paralyzed by the Joker.