"How I Got That Name" is divided into four stanzas. It's told by a first person speaker called, appropriately enough, Marilyn Mei Ling Chin. In the first paragraph she recounts her father's journey to America from China, and touches on how she got her American name "Marilyn" (her dad was obsessed with Marilyn Monroe, apparently—who wasn't?). The second paragraph describes some of the difficulties of growing up in America as a Chinese-American, including having to deal with stereotypes such as the "Model Minority" stereotype.
The third verse paragraph focuses on the speaker's relationship to her Chinese ancestors. The speaker then imagines herself dying (yeah, because that's just fun to do). In the final verse paragraph of the poem, the speaker talks about herself in the third person, imagining what would be said about her at her death, in a eulogy given at her funeral.