He refuses to sign the confession because, in the end, his name is the only truth he has left. He was not faithful to his wife and has worked hard to make amends. After all the lies and deceit flying around Salem, John's name is all he has left of his self-worth. I am not entirely sure but this is the best answer I can give! hope this helps! ^^
In the gift of the magi the summary is giving up something that means a lot to you for someone you love because even when something is so important to you a loved one means more
Im 99% sure that it is metaphor