What distressing information does the man who tattoos Hannah give her?

The man tasked with tattooing the women, himself a prisoner, asks Hannah her name. She replies that it is Chaya Abramowicz. He tells her that she is wearing his daughter's dress. Her name was Chaya, too. He says to never forget her prisoner number and to live for all the Chayas of the world.

The man told Hannah that she was wearing his daughter's dress and that his daughter's name was Chaya too.