The Story of a New Name is the sequel to My Brilliant Friend, the first book in Italian writer Elena Ferrante’s world-acclaimed quartet of Neapolitan novels. The second book in the quartet continues to document the friendship between Elena Greco and Lila Cerullo and opens in 1966 when first-person narrator Elena, burdened by the contents of the notebooks that Lila has entrusted to her, throws all of them into the river Arno in Pisa (where Elena is studying).

Elena narrates the events that immediately follow the ending of My Brilliant Friend. Lila, who has just married Stefano Carracci, discovers that her new husband has betrayed her trust by giving the shoes she made for him to a man she loathes, Marcello Solara. From that moment, Lila feels contempt for her husband and does everything in her power to repulse his sexual advances and humiliate him. Stefano responds with a mixture of cajoling words and beatings, eager to assert his authority over her.

Elena meanwhile, continues her studies, which she struggles with in the aftermath of Lila’s wedding. Elena’s crush on the handsome, intellectual, and seemingly inaccessible Nino Sarratore first sabotages and then wrecks her romantic relationship with another neighborhood boy, Antonio Cappuccio. The final straw for Antonio comes when Elena enlists the help of the Camorrist Solara brothers to exempt Antonio from military service. Though Elena is depressed about Antonio abandoning her, she flourishes without him at school, and a prominent teacher, Professor Galiani, praises Elena’s writing. 

Elena rents a house in Ischia with Lila, Lila’s sister-in-law Pinuccia, and Lila’s mother Nunzia. The group makes the trip because a gynecologist told Lila, who has struggled to get pregnant and suffered a miscarriage, that swimming can boost her strength and fertility. For her part, Elena chooses the island of Ischia over other potential seaside resorts because Nino is staying there with his friend Bruno Soccavo. The young women begin to see Nino and Bruno every day at the beach. At first, Nino and Lila are shy towards one another and prefer to talk through Elena, but they soon embark on a passionate affair. Elena, who is hurt by this development, nevertheless helps the couple to spend a night together by making an excuse about visiting an ailing teacher in Barano. While Nino and Lila are together, Elena stays in Barano and loses her virginity to Nino’s womanizing father, Donato Sarratore.

On returning to Naples, Elena applies herself to her studies, resolving to forget about Nino and Lila as much as she can. She successfully obtains a scholarship to the prestigious Pisa Normale after her high school graduation. Meanwhile, Nino and Lila meet clandestinely in the store where she works. When Lila becomes pregnant, she concocts an escape plan for herself and Nino, renting a house in Campi Flegrei. While Lila is delighted with the relationship and the renewal of intellectual pursuits it inspires, Nino, who is a serious student, begins to find Lila overbearing. He leaves her, and he’s discouraged from returning to Lila by a disguised Antonio Cappuccio, whom Michele Solara has sent to track the couple down. When Antonio beats Nino, warning him to never go near Lila again, Nino obliges. Meanwhile, Enzo Scanno, Lila’s childhood friend and admirer, goes to Campi Flegrei to retrieve her and bring her home to Stefano.

When Lila’s baby, little Gennaro, is born, she is a devoted mother and learns to tolerate Stefano as best she can. Stefano, however, is miserable in the marriage. He pursues an affair with Ada Cappuccio. When Michele Solara, who wants Lila for himself, insists that Stefano must choose between the women, Stefano chooses Ada. With Solara’s help, Stefano procures an apartment for Lila and Gennaro; however, because Lila knows that assistance would put her at Solara’s mercy, she rejects it. Instead, she enlists Enzo Scanno’s help, and together they move to San Giovanni at Teduccio. There, they live in poverty. Lila must take a demeaning job in Bruno Soccavo’s mortadella factory. In the evenings, she assists Enzo with his advanced mathematics studies.

Elena, meanwhile, has become engaged to Pietro Airota, a serious student she meets in Pisa while drafting a novel. Pietro’s mother, Adele, takes Elena’s novel to a publisher. At a reading of the novel in a Milan bookstore, one of the guests present is Nino Sarratore.