You hit the nail on the head when you peg this novel as a search for identity. Rachel, the main character, has had a great tragedy: her mother and siblings fell from a tall building to their deaths below. As a result of this tragedy, Rachel is moved all around and, most specifically, to live with her grandmother where she struggles to become who she is. Rachel finally "finds" her identity by connecting with friends such as Jesse and reestablishing the connection with her surviving family members.
Why does Rachel have trouble with identity in the first place? Well, apart from losing all of her immediate family, Rachel has an interesting racial mix that causes her not to fit into either the "white" or "black" group at school. Being a child with dark skin and blue eyes, neither group accepts her. Rachel, therefore, begins to create her own labels of where she fits: as a girl who will always be "just fine" and/or a girl who concentrates fully on her studies.
I'm not the color of my skin. I'm a story. One with a past and a future unwritten.
In this quest for identity due to "the color of my skin," Rachel finds her identity within the friend of Jesse. Rachel meets Jesse when she begins working at the Salvation Army. Jesse is white, but knows more about black culture than anyone Rachel knows. The fact that someone like Jesse even exists, helps Rachel understand that there are people who are like her in the world.
We live in the same house but we both feel lonely. We and lonely don't belong in the same sentence.
As you can see from the quote above, it isn't only friends who help Rachel find her identity. It is also Rachel's surviving family members, most especially her grandmother. This quotation can be deemed the turning point of this relationship. There is no reason why two family members should live in the same house and be lonely. The two work their differences out from here and begin to live life as a family. Being a family within her grandmother's household helps Rachel find her identity.
In conclusion, the reader should realize that Rachel "finds" her identity in the context of friends and surviving family members. I must admit, however, that I find the wording of "finding" an identity strange. Why? An identity is there all along, it is more of the attempt to identify or realize or name or label an identity that fits. The word "finding" assumes one must "go and look" for something. In reality, in this case, Rachel's identity has been within her all along. Rachel's grandmother and friends like Jesse just help her realize that very fact.