"Dusting" by Julia Alvarez

The speaker of this poem has the persona of a child; a child coming of age and becoming more aware of his of her surroundings. They want to be heard in the worst way. "Each morning I wrote my name." The speaker does this everyday only to have it dusted away by his or her mother. The last stanza of the poem proved to be the most poignant for me, "My name was swallowed in the towel...her, anonymous," that part surprised me a bit. The speaker seemed to be challenging his or her mother's authority because the name was written every morning, but the mother kept on erasing the name. The name was a way of establishing identity and a fear existed in the destruction of the "art," he or she did not want to "be like her, anonymous." I just have one question. Does the title refer to the actual erasing of the speaker's name or does it represent the dusting of the mother's identity making her anonymous?