The speaker imagines the woman is erasing names because he himself is having trouble facing the reality of the war.
The poem describes a Vietnam veteran who looks at the memorial and imagines the ends of the different men he saw die. At the end, he imagines a woman erasing names, but she is really not.
In the black mirror
a woman's trying to erase names:
No, she's brushing a boy's hair.
The soldier is facing his past, and what happened to him in the war. He is facing the loss of all of the soldiers who did not come back with him, or who lost limbs like the man who looks into his eyes. He wants to erase the names, and erase the events that caused them from his memory.
The theme of the poem is moving on with one's life, and coming to the reality of one's situation. The speaker does not see the memorial the same way other visitors do, except other soldiers. He may not have died or lost limbs there, but he lost part of himself. He needs to come to terms with that, and move on with his life after facing it.