My name is Monster by Katie Hale

After the Sickness has killed off her parents, and the bombs have fallen on the last safe cities, Monster emerges from the arctic vault which has kept her alive. When she washes up on the coast of Scotland, everyone she knows is dead, and she believes she is alone in an empty world. Monster begins the long walk south, scavenging and learning the contours of this familiar land made new. Slowly, piece by piece, she begins to rebuild a life. Until, one day, she finds a girl: feral, and ready to be taught all that Monster knows. Changing her own name to Mother, Monster names the child after herself. As young Monster learns from Mother, she also discovers her own desires, realising that she wants very different things to the woman who made, but did not create, her.