This has come up a few times, but because our social circle irl is predominantly Pokemon and we have that as a special interest, we loosely have a collective Pokemon Trainer or broadly Beastmaster archetrope. I fit this more strongly personally, but it's also a common enough theme in our system that I'd count it as up there for collective identities. We love any collectable mon stuff, especially if there's an easily accessible physical element of it. That's why we love collecting TCGs because they're so easy to get and store, and playing physical tournaments turns into a tangible thing we can do with them. We also collect Pokemon figures and toys. This also extends to why we also collect Bakugan and things like that. Though physical accessibility is still a big thing and so we don't have a lot of big, specific collections outside of Pokemon, but we have a lot of little guys from stuff like Moshi Monsters, Beyblade, Neopets, and a lot of it is because we've found them while thrifting.
To us I think this also stretches what counts as a "mon" or the subject of a Beastmaster. Because we've gotten more into the Cookie Run TCG, the characters to us feel closer to that, but that's not remotely how the actual game treats them. It comes down to I feel a specific summoner attachment to it and thus in my brain they become that. It's like Herb Cookie winds up being a battle species instead of a character.
For some reason this is only a thing with physical media though. Even though we play a lot of video games we don't feel as strong of a draw with digital media, but I think that might be because we wind up replaying/resetting a lot of games. We'll still generally lean towards creature collecting games or like playing as Beastmaster characters (most recent example I can think of is Ochette from Octopath Traveller II). I think it's also having some kind of tactile thing makes it feel more grounded and real to us since we're otherwise very hands on.