why no name for curlys wife

Curley's wife is a possession. She represents such loneliness that she doesn't even get a name. Curley is abusive although we never see them together. She spends much of the time "looking" for Curley although she is really looking for other companionship.

Whenever Curley's wife shows up we see her loneliness. It pours out of her in resentment and disillusion.

"I never get to talk to nobody. I get awful lonely."

"What's the matter with me? Ain't I got a right to talk to nobody?"

"Seems like they ain't none of them cares how I gotta live".

Try to read what she is saying here. She blames others (rightly so) but feels so disenfranchised that she does not know who she is anymore.