What does it mean when someone says, "speak and give your child a father" to Hester?

In Chapter Three, Reverend Dimmesdale and the other ministers attempt to compel Hester to name her co-sinner, the father of her young baby.  Although she has just been released from prison and is beginning the next stage of her punishment for the crime of adultery, she refuses to give his name because she would prefer to "'endure his agony, as well as [her own].'"  

Someone from the crowd yells to her on the scaffold to "'Speak; and give your child a father!'"  This person obviously believes that the appropriate thing for her to do is confess the name of her child's father because her child will never be able to have a father if she is unwilling to name the man.  Only if she speaks his name will he be able to come forward and claim his place as the father of her child, a position that is his responsibility.  Hester's response is that her child will have her heavenly Father, and that is all.