Why did the peddler sign himself as Captain von Stahle?

Throughout his life, the peddler had never known respect. He was always treated coldly by the world. For the first time in his life, he was honored and respected as if he were a captain. Even after the truth was exposed, the daughter continued to treat him in a similar way. The way he was treated encouraged him to behave in a like manner. He signed the letter as Captain von Stahle so as to underline the impact of Edla's goodness on him.

The ironmaster has invited the peddler to his house mistaking him for Captain von Stahle. He was welcomed there and looked after as captain even after the reality became known. The peddler got a chance to redeem himself from dishonest ways by acting as an honourable Captain.