I think we should have the Batfamily treat the batarangs like business cards. For both branding and comedic purposes. I’ve only really seen the bats having personal batarangs a few times. Like yeah, they all usually use the company provided stock batarangs, but they also have their own personal ones that they use if they really need to send a message of who threw it. (Or pass the blame for throwing it by using someone else’s).
Imagine a league member meeting some random Batfamily member for the first time and asking for an autograph and then they pull out a business card holder filled with batarangs. I’d imagine Steph doing that (they’re pre-signed and have an professional looking address that leads to a Waffle House), and when questioned she’d just say “It’s important to make a good impression when making connections and a good business card can help keep you in people’s mind” just quoting something Bruce probably told her once.
Here’s some ideas on how I think they could look. Obviously Batman has the stock batarangs along with all the evolutions it’s gone through over the years, nightwing has his Wingdings, but the one that can drive personalized rangs home are the Robin disks, because it feels like it’s really back and forth whether robins have their own designed rangs or just use the bat ones. Spoiler and signal could use purple and yellow ones, and I imagine red hood uses the red bat emblem on his chest. Orphan’s could look like stock batarangs at first glance but upon close inspection you’d find the stitched mouth design embossed or engraved in it. Red Robin I feel like would either keep using Robin disks but red or he’d redesign them using his “double R” logo.
I got nothing for the extended Batfamily since I haven’t read pretty much anything with them but off the top of my head I’d imagine Kate using batarangs that are outlined with red like her hair.