There are different factions in this book: witches, bears, gyptians, and scholars, and each has its own separate and distinct group identity. Then of course there's Lyra, a young girl struggling to figure out just who she is and where she fits in. Her task is only made more difficult when she finds out who her parents are and doesn't like them. Lyra's transformation from innocence to experience is chronicled through the His Dark Materials trilogy. In this first book we see her interacting with various groups (gyptians, bears, witches, scholars, Gobblers) and trying out different social roles.
Lyra is a chameleon; she can easily pretend to be a part of different groups, including gyptian and bear societies, but in the long term she doesn't actually fit in.
Since Lyra didn't grow up knowing who her parents were, they didn't impact her identity at all.
Lyra's parents impact her identity because they are a strong example of what she could be, but doesn't want to become.