Reddit mentions of My Name Is Memory

Might be My Name is Memory, by Ann Brashares. This page on Google Books mentions heroin

>Primarily known for her young adult Traveling Pants series, Brashares offers her second adult novel (The Last Summer (Of You and Me), 2007), about a man who remembers his past lives and the woman he's loved through them all.In 2004, Virginia high-school student Lucy develops an obsessive crush on a mysterious new classmate, Daniel. They finally share a kiss at the Senior Ball, but then Daniel calls her Sophia and insists that they have loved each other for centuries. A frightened Lucy runs away, leaving Daniel bereft. He has spent most of his many lives trying to find Sophia, ever since their disastrous first meeting during his first remembered life. As a soldier in North Africa in the sixth century he mistakenly burned down a house (think civilian casualties in Afghanistan), causing a little girl version of Sophia to die—his "original sin." Two hundred years later in Asia Minor, Daniel helped the woman her soul then inhabited escape from her abusive husband, Daniel's older brother Joaquim, who then killed him. Throughout the centuries when Daniel and Sophia have met, their ages or circumstances usually kept them apart. However, during World War I Sophia/Constance was his nurse and sweetheart at a British military hospital where she hid a letter of explanation about Daniel to her future self. Fast forward to 2006. Attending college, Lucy has lost track of Daniel. Then a psychic shocks her by bringing up Daniel by name. Now driven to find the truth through hypnosis and the Internet, Lucy finds the WWI letter and accepts her pasts. But she can't find Daniel. Unfortunately, menacing Joaquim is on Daniel's trail too. Plenty of grown up "Pants" fans will swoon for this hokey but undeniably effective romance, and an ambiguous ending leaves the door ajar for a sequel. (Kirkus Reviews, March 15, 2010)