Why does the policeman not tell Bob that he is the real Jimmy Wells in the story "After Twenty Years?"
The policeman on the beat does not reveal his true identity to Bob because he recognizes his old friend as a wanted man.
Since the two friends parted twenty years ago, their lives have certainly taken different directions: whereas Jimmy Wells has become a policeman Bob a/k/a "Silky Bob" is a criminal. So, when Jimmy recognizes his old friend as a man on a wanted poster, he cannot professionally reveal himself to Bob because this wanted man might flee or overtake him. (At the turn of the century, the setting of this story, beat policemen did not carry guns; they had a whistle and a baton only.) On a personal level Jimmy Wells does not wish to identify himself to Bob and cause him the embarrassment of being arrested by an old friend.
Having ascertained that Bob will wait in the doorway, Officer Wells returns to the precinct and asks a plains clothes officer to arrest Silky Bob. In addition, his note to Bob that mentions "Somehow I couldn't do it myself" indicates that Jimmy just did not have the "heart" to arrest his old friend and humiliate him in this manner.