In John Steinbeck's short story "The Chrysanthemums," the tinker represents society. His way of life greatly appeals to Elisa. She shares her dreams with the man:
"I've never lived as you do, but I know what you mean. When the night is dark—why, the stars are sharp-pointed, and there's quiet. Why, you rise up and up!...
"You sleep right in the wagon?" Elisa asked.
"Right in the wagon, ma'am. Rain or shine I'm dry as a cow in here."
"It must be nice," she said. "it must be very nice. I wish women could do such things."
"It ain't the right kind of life for a woman."
In this part of the story, the man represents the societal expectations that prohibit a woman from reaching for her dreams as a man was able to do. It is important to remember that Steinbeck wrote the story in 1934 when a woman was expected to be a wife and mother, not a "free spirit." Eliza is not a traditional mother: she has no children. However she does have her chrysanthemums—they are her children. She loves them and tends to them carefully. Although she is distant when the tinker first arrives, it is his feigned interest in her flowers which enables her to open up. She offers the man some work, and chrysanthemum sprouts for "a lady down the road."
However, later, as Eliza and her husband drive into town, Eliza is crushed to find her gift of her flowers tossed aside along the road where the tinker had passed earlier.
Far ahead on the road Elisa saw a dark speck. She knew...
"He might have thrown them off the road. That wouldn't have been much trouble, not much..."
As her husband drives on, he doesn't realize what has transpired, but the narrator tells the reader...
She turned up her coat collar so he could not see that she was crying weakly—like an old woman.
The tinker did not care about Elisa's flowers; he is only interested in getting her business.
The man does not have a name because he represents a society that does not value a woman. He also is not given a name because it symbolizes his lack of interest in Elisa and what she loves. He pretends to so that she will give him work. As his interest is superficial, he is not interested in knowing her. There is no exchange of names because he will not visit again. He has gotten what he wants, but their interaction means nothing to him. It has no depth: he is the shell of a man, representing a society that does not care for her. He could be any man in that time who saw no reason to respect or connect with a woman as a person. It's business and that's all.