My Name is Leon is set in the United Kingdom during the 1980s. It starts by introducing readers to nine-year-old Leon, who witnesses his mother, Carol, wrestle with her worsening mental health issues. Despite his young age, Leon often finds himself acting as his mother and baby brother Jake's primary caregiver. Due to their mother's inability to cope, both children end up being taken into the foster care system, angering them both.
While in the foster care system, the two brothers are split up as a matter of necessity. Jake, who is white, is swiftly adopted by a family who can't conceive a child of their own. Leon, on the other hand, because he is mixed-race, faces more challenges. Initially, he is placed under the care of a woman named Maureen, an experienced and kind-hearted woman with experience taking care of foster care kids. With her, Leon navigates his complex and oftentimes overwhelming feelings about why he hasn't been adopted like his brother.
Leon's primary goal throughout the novel is reuniting with Jake. He meticulously saves money and hatches plans to work his way back into his brother's life. However, during his time with Maureen, Leon also discovers the world of allotments (community gardens), where he begins to care for plants of his own. Through the allotment, he meets Tufty and Mr. Devlin, both of whom have a significant impact on his life.
As Leon grows older, he becomes increasingly aware of the riots and racial tensions unfolding in Britain. He has a realization that he has been treated differently than Jake because of his race, which helps him understand race and racial tension across the world after he discovers that his father, a Black man, was involved in racial protests, strengthening Leon's resolve to join them.
Suddenly, Maureen falls ill, and Leon is sent to live with his sister, Sylvia. Jake becomes more uneasy and decides to run away from his sister and towards Jake. Leon manages to be away for a while, but he is ultimately reunited with his sister.
In the end, Leon has begun to form a makeshift family with the people around him, from the allotment regulars to his foster family and his sister. Though he's not yet reunited with Jake, Leon is in a much better place than he ever was.