Why is the old man in "The Chaser" nameless?

The author probably had at least two reasons for not assigning a name to the old man. One was that the old man was engaged in an illegal business and probably preferred to remain anonymous. There are a lot of people doing business under false names or fictitious corporate names because they are engaged in illegal enterprises or are trying to evade paying taxes. Not every business is what it looks like on the outside. The old man is probably dealing in cash only and is thereby avoiding paying income tax, self-employment tax, and having a business license requiring annual renewal fees and local business taxes. He is keeping a very low profile. This adds to the dramatic effect of the story.

But there is another reason why John Collier didn't want to assign an name. Most authors find it a nuisance to make up names for characters and only do it when necessary. If there are a number of characters in a story or novel, then the author has to give them names. It is a hard job to think of appropriate names for characters, and not many authors were really good at it.

This brings up the question of why Collier gave the customer a name. For one thing, the old man is very cautious about the people he does business with. He would not accommodate Alan Austen at all, or tell him about his "chaser," if he didn't know who he was. Alan Austen could have been a cop. We see that Austen has to identify himself with a card. This would be a card given to him in confidence by a former client of the old man. The former client would have scribbled an introduction on the back of his own card.

An old man sat in the rocking-chair, reading a newspaper. Alan, without a word, handed him the card he had been given. "Sit down, Mr. Austen," said the old man very politely. "I am glad to make your acquaintance."

We see in a story such as "Hills Like White Elephants" by Ernest Hemingway that an author can get along without giving any of the characters names. The two main characters are of opposite sexes, so he can call one "the man" and the other "the girl." The woman who serves him is "the woman." We hear incidentally that the man is American and that he sometimes calls the girl "Jig," which doesn't tell us much except that they are pretty well acquainted.

I don't believe that John Collier had any other purpose for not giving the old man a name. It wouldn't help us to visualize him if we knew his name. We visualize him as an old man. If he did use a name, it probably wouldn't be his real name anyway.