There may be any number of reasons for this choice to leave the characters without names. The main reason may have to do with the high stakes of survival in this post-apocalyptic world, when people are willing to kill other people over food. In some cases, people are killing other people to provide food, i.e. cannibalism. This dehumanizing behavior of most of the book's characters, the survivors of a vaguely-described apocalypse, echoes the author's decision to leave characters unnamed.
There is also a suggestion that the main characters may or may not be related, i.e. the boy calls his father "Papa" but it may be that the man has been taking care of the boy simply because the boy needed someone. This idea finds validity at the end of the novel when the boy is readily taken in by another family. This fluidity of family ties is connected to the lack of specific names: family is no longer defined by blood relation or history but by situation and timing, as well as practicality and need.
Just as some people in this world treat one another with brutal detachment, others think of people as family and worthy of protection and kindness. In the first example, lack of names denotes anonymity and lack of humanity; in the second, it shows that compassion is to be shared among humanity regardless of duty or family bonds.