Why didn't the other characters have any names? Why do you think their names weren't mentioned?
There could be many explanations for this. One potential reason would be to enhance the universal feel of the work. In writing this story in 1941, Clark is witnessing the effects of the Second World War, where nations committed themselves to the annihilation of other nations and civilizations. In a war where 60 million soldiers and civilians died, there could be a compelling case that the world, as one knew it, was going to come to an end. The story's feel of a world that has ended in overall catastrophe, mirroring the events of the time period. In not naming any of characters, the feeling is that these individuals could be from any nation, any ethnicity, and the common bond between them is that the world and civilization has come to an end. The resulting world is one that they all share and in which struggling for survival seems to be a perquisite. Names in this setting are irrelevant for the struggle to live is the defining element for all of them. Ironically enough, the only "named" items are the books/ literature saved as well as the phonograph. These items that help to make life more livable and help to give meaning to life are the only things that earn the distinction of having names. Seeing that human beings are the cause for this end, it makes sense that they lose their right to have any names attached to them.