"How I Got That Name" is a poem written in four stanzas in a form of poetry called free verse. Free verse is pretty much what it sounds like: a poetic style that doesn't stick to any regular meter or rhyme scheme. It was popularized by the American poet Walt Whitman, and it's used in a lot of contemporary poetry.
The free verse form of "How I Got That Name" means that Chin gives herself a lot of freedom to change things up in the poem. For one thing, there aren't the same number of syllables in each line. If we take the lines, "somewhere between Angel Island and the sea,/ when my father the paperson/ in the late 1950s" (8-9), we can see that the length of each line (and the number of syllables) varies. There are eleven syllables in the first line, eight in the second, and seven in the last. See a pattern there? Yeah, neither do we. What's more, the four stanzas vary pretty wildly in length. The first verse paragraph is the longest, with thirty-five lines, and the third is the shortest, with only sixteen lines.
So what's up with this choice? Why go with free verse? Well, free verse is the way to go if you want to mimic the patterns of informal speech. We don't really speak in predictable patterns, do we? Well, maybe this guy might. So, by choosing free verse, Chin creates an informal, conversational tone in her poem. It's like she really just laying all this out to us, as a friend might. As her readers, we feel connected to her on a more personal level than if she were putting all these ideas in, say, a sonnet or a villanelle.