Roger Chillingworth has to change his name because he does not want the town of Boston to know that he is Hester Prynne's husband. Hester has not been sentenced to death for her crime of adultery (sleeping with someone other than her husband) because her judges cannot be sure that her husband is actually alive; if he is dead, then she has not actually committed adultery—if he is alive, then she has. The penalty for adultery is typically death, as we learn from some of the Boston women who have come to see her upon the scaffold. If Chillingworth reveals that he is Hester's husband, then the doubt about her adultery will be erased and she could be put to death. He does not want that. In addition, he wants to keep his identity a secret so that he can pursue her co-sinner, the father of her baby daughter, so that he can punish this man for his crime against them both.