the name had been changed somewhere between Angel Island and the sea (7-8)
The speaker's discussion of her name change points to how her identity was transformed by her family's coming to America. She was no longer "Mei Ling" but "Marilyn," and this change suggests all the cultural and geographic changes that she also had to face as a result.
[…] life doesn't' hinge on that red, red wheelbarrow, but whether or not our new lover in the final episode of "Santa Barbara" will lean over a scented candle and call us a "b****." (50-55)
The speaker's reference to the soap opera "Santa Barbara" here suggests just how influenced by American culture she becomes as a result of her move to America. Her interest in American TV shows how her identity has shifted, from Chinese to American.
And I, his least favorite— "not quite boiled, not quite cooked," (66-67)
In these lines, the speaker imagines her forebear, Patriarch Chin, looking down on her and being very displeased. That's because the speaker is "'not quite boiled, not quite cooked,'" meaning that she is neither one thing nor the other: she's neither American nor Chinese. Her identity is confused.
[She was] just another squatter in her own bamboo grove minding her poetry (84-85)
In referring to herself as a "squatter," the speaker again points to how her identity is uncertain. As a "squatter," she's someone who doesn't have her own home, but lives in the homes of others.