Curate, connect, and discover
In all honesty Bruce had never really intended for Billy to always be a substitute for when Damian was sick or not available to go out as Robin. It just so happened that Billy was almost Always available to fill in as Robin.
Usually he would only have Billy fill in when none of his other children were patrolling, he didn’t need to hear them complaining about him adopting another Black haired Blue eyed child. (He tried it didn’t work) but unfortunately Dick decided to suit up that night and ended up running into Billy and Bruce, Well Robin and Batman.
At First Dick been shocked that there was another Robin, Did Damian know? Did Alfred know was honestly the more important question. Of course he knew he was most likely the one who made another costume for the poor kid!