In John Steinbeck's story Of Mice and Men, Curley's wife does not have a name. I don't believe that in the novel this has any social significance—such as women having a secondary role in society, etc. Quite simply, Steinbeck's story is about two men trying to survive in a man's world: from a social standpoint, the conflict they face is with society (which is governed by men) and with individual men on the ranch. I believe that Steinbeck includes this woman as a "flat" and "static" secondary character that drives the plot and that is all.
This story is about George and Lenny. We learn of their problems in the Salinas Valley—they are run out of Weed because Lenny gets too physical in trying to feel the softness of a young woman's dress: another unnamed female. When they arrive at the ranch, they have a chance to make a new start. George has been coaching Lenny—a large man who is slow to learn and fails to understand important rules within society. Curley's wife is someone George warns Lenny about. Like a phantom, she moves in and out of the story, reinforcing the mood of disaster waiting to happen. The most important element that Curley's wife adds to the story is one of danger and fear. When she is around, the men are nervous and tell her to leave. Curley could fire any one of them if he thought any man was flirting with his wife. These men are in dire enough straits that they won't even speak to the woman if it means they could lose their job.
As George struggles to guide Lenny, and Lenny struggles to remember the things George has told him, the dream of a new life shimmers in the distance for both George, Lenny, Candy—and possibly even Crooks. However, the story is firmly placed in an era where dreams have been crushed for thousands of people (because of the Great Depression). When Lenny kills Curley's wife, it is an accident, but her death has served its purpose: hopes of a new life have been destroyed, and George is forced to show how much he cares for Lenny by "saving" him from the angry men chasing him because of the death of their boss's wife.
Steinbeck includes Curley's wife to reinforce the story's dark mood, and to act as a catalyst to create an insurmountable conflict that brings the story to a close. As a "literary device," her name is not important, but what she does—and causes Lenny to do—is central to the story.
Steinbeck might not have given any of the men names if he didn't have to, but there are many male characters in his story and he has to differentiate them as much as possible, especially since they are all working men dressed in work clothes. Furthermore, the author planned to adapt his story to a play, and he did so the same year the book was published, which was in 1937. (See the eNotes Introduction by clicking on the reference link below.) The male characters on the stage would have had to have names for the audience to be able to tell them apart. You can see in the novella that there is a great deal of "naming," as is invariably in the case of stage plays. Characters introduce themselves by name, call other characters by name, and introduce characters to other characters by name. A good example is to be found in the second chapter when the boss comes in to sign up the new men.
The boss licked his pencil. "What's your name?"
"And what's yours?"
George said, "His name's Lennie Small."
This sort of tedious dialogue is solely for the purpose of identification.
On the other hand, there is only one female character in the story and in the play. That is Curley's wife. There is no need to add yet another name to all the other names because it would only tax the reader's or viewer's memory further. It might even create confusion, because if some men referred to her as, say, Agnes and others referred to her as Curley's wife, a reader or viewer might get the impression that there are two different women on the ranch.
Steinbeck typically portrays women as being useless and only troublemakers. So neglecting to give Curly's wife a name simply furthers the extent of her insignifigance in the story.