She looked out the window her whole life, the way so many women sit their sadness on an elbow.  I wonder if she made the best with what she got or was she sorry because she couldn't be all the things she wanted to be.  Esperanza. I have inherited her name, but I don't want to inherit her place by the window. 

The above quote is not my favorite quote from this story, but it is incredibly memorable.  It's memorable because the imagery of the woman sitting by the window is a reoccurring image throughout the story.  It's not a positive image either.  Esperanza interprets that image as showing how trapped women are in their lives in her neighborhood and her culture.  It's an especially sad quote because of how it foreshadows Sally's future, which ends up being worse.  She is not even allowed to look out of the window.  

Identity is a major theme of the novel, and Esperanza spends a lot of time struggling with her personal identity.  

In English my name means hope. In Spanish it means too many letters. It means sadness, it means waiting. It is like the number nine. A muddy color. It is the Mexican records my father plays on Sunday mornings when he is shaving, songs like sobbing.

Esperanza does not like her name, because it singles her out as different.  Non-Hispanics struggle with the name, and she doesn't see it meaning hope at all.  To Esperanza, her name is further cause for her suffering.  

Related to the theme of identity and loneliness that Esperanza feels about her name is this quote:

I would like to baptize myself under a new name, a name more like the real me, the one nobody sees. Esperanza as Lisandra or Maritza or Zeze the X. Yes. Something like Zeze the X will do. 

Like all kids do at some point, Esperanza is playing around with different names.  But Esperanza is serious.  She really, really wants a new name in order to more accurately reflect the person that she believes she is.  

I'll stick to memorable quotes about identity.  The following quote focuses on racial identity.  

All brown all around, we are safe. But watch us drive into a neighborhood of another color and our knees go shakity-shake and our car windows get rolled up tight and our eyes look straight.

Esperanza is acutely aware of her ethnicity, and this quote points out that it affects more than just her.  Many members of her community are aware of their race and feeling different in certain parts of the city.