I'm not sure about this question, not because you put it wrongly (also this is a discussed topic), but because I feel like "identity" is a bit too much connected to how much we know a group. I don't want to make names but for me the vast majority of bgs who do dark concepts are basically interchangeable at a first sight and first listen. This doesn't mean they are actually the same, but sometimes we say things like "this song could be sung by another group and it wouldn't make a difference" but I feel like this applies to a lot of groups. The majority, with just some rare exceptions.

For example, a group that commonly people say have an identity and we all know they are damn good: Red Velvet. I'm not that sure that at least half of their title tracks couldn't be have perfectly executed by others (I mean, Red Flavor was a Little Mix refused song) in a parallel universe, of course modified. Red Velvet surely make them work perfectly, but unless there is a very innovative and basically undone concept or sound (Dreamcatcher for example, or 2NE1 at their time, or f(x)), I think we could say that a lot of groups "don't have an identity" and just do very well a lot of things. It's just that Red Velvet has a name for themselves and people recognize them as a result. I hope this makes sense.

I mean, as an identity, I don't think Blackpink or Red Velvet with their "dual concept" (which often lead to many more shades) is that different from the vast majority of "let's see what we could do" groups at the end of the day. I feel like the heart of the group is made by the voices and the confidence of the members and how well they execute their concept, but until you know the members, they still are interchangeable if we exclude some notable exceptions which aren't even necessarily the best groups, just very peculiar.

I wouldn't say Girls' Generation have had an "identity" ad people mean it in these answers, they did a lot of things left and right and then back again and at the same time, but this doesn't reduce how well they did these things and how they were perfect for all these concepts and their legacy.