
r/BatFamily

Damian and fragrance
So IDK if anyone else head canons this but imma share it anyway.
I head canon that Damian is extremely particular about fragrances and hygiene. Not in the he hates perfumes and such. But more in the it bothers him very deeply to be around cheap smells and cheap soaps. Because of his deeply Arabic roots and the routines that he grew up around with Talia and Ras Al Ghul who both took fragrance and cleanliness very seriously. So perfumes, colognes, soap and laundry soap are something he's extremely particular about.
So I just picture 10 year old Damian going with Cass, Steph and Babs to go buy perfume and body mist. But it's not what Damian is used to and due to the fit he absolutely had. He can only go fragrance shopping with Selina because she gets it.... Babs, Cass and Steph each end up getting new perfumes every time he goes with her. Because he sees them as family and despite how he may act at times he does genuinely care and believes they deserve the best.
.... The day he saw Tim using something like axe body spray.... Ooooh boy was that a tantrum from hell. Now Tim has like 8 different colognes. Some different soaps and a whole new laundry detergent. Because Damian refused to "let Drake embrass the family."
Bats making friends and their secretiveness
Barbara tries to keep her identity as Batgirl or Oracle secret from her friends and family, including her father. In pre-Crisis comics, Jim had to tell his daughter that he had found out that she was Batgirl.
Bruce usually has girlfriends to hide that Bruce is Batman. Even when he has cares about his girlfriend, the relationship always falls apart because he won't tell them that he's Batman and they're upset at how often he ignores them as Batman is the most important part of his personality, not Bruce. Julie Madison was his longest-lasting girlfriend because she began getting to know Bruce before he became Batman and he tried to treat her as important even though he refused to show her his identity as Batman. Bruce eventually admitted that Batman was more important to him than his relationship with Julie and initiated a breakup with her. Bruce's only real friends are the superheroes he's friends with as Batman.
Cassandra is only willing to get to know people as Batgirl, not as Cassandra. Even after all of the effort Barbara and Stephanie have put into convincing Cass that she's a good person and not a threat when she's Cassandra and not just when she's Batgirl, she still only exists as Cass when she's with the bats or the Birds of Prey, focusing on Batgirl as the most important part of her identity. She's been convinced by Barbara and Bruce to keep secret the fact that Cass is Batgirl but, unlike Bruce, she's unwilling to have civilian friends who know of Cass but not Batgirl. If someone, like Ba Bao or Stephanie, insists on regularly interacting with her and possibly forming a friendship, she makes sure they're interacting with Batgirl. Cass is the only bat who doesn't know how to make friends. People have to make friends with her and force her to recognize that they consider her to be a friend. She's not willing to have a friend who doesn't know why she gets injured and spends lots of time away from them. She already ignores Steph when she's upset and I suspect that she'd be worse than Bruce when it comes to civilian friends who don't know that she's Batgirl.
To the best of my knowledge, Damian hasn't been shown interacting with civilians other than his early time with Colin.
Dick is willing to make friends who don't know that he's Nightwing but they usually find out about his secret identity. I suspect that he doesn't like keeping it secret from his friends and wants them to find out.
Duke refuses to have friends and family who don't know that he's Signal. He's the only bat who refuses to even pretend to follow Bruce's advice to keep his identity secret from his friends and family. When his mother woke up from her coma, he insisted on telling her about his hero identity.
Stephanie tried to keep her identity as Spoiler secret from her mother and the few civilian friends she made. In Batgirl (2009), she was still trying to keep her mother from catching on to her identity as Batgirl.
Tim is able to make friends as Tim and maintain them even when they don't know that he's Robin. He's more successful at being Robin and having a civilian life with friends who like him as Tim than any of the other bats. His lack of sleep is probably part of that as it allows him to protect people as Robin and interact with his friends as Tim. He's only willing to tell his friends and family that he's Robin if Bruce approves though he complains to Bruce about his close friends not knowing his secret.