"Beyond Bedlam", a 1951 novella by Wyman Guin. You can read it at the Internet Archive. Here is the ISFDB synopsis:
A story about a world where everyone is schizophrenic. Everyone has a side personality. Everyone is using compulsory drugs to separate and control the personalities. Apparently going to this kind of lifestyle prevents all wars and violence. The two personalities everyone has are called hypoalter and hyperalter and the prevalent personality is switched every five days. Both personalities of the protagonist are married to the same woman (to her separate personalities), which in itself is uncommon and is considered to be slightly perverted. And what is really kinky is that the hyperalter of the personality has an affair with the wife of the hypoalter. That kind of perversion can't end well.
The alter ego's name is Susan Shorrs, I think.
Mary was glad to find Captain Thiel, the nice medicop, on duty. But she was silent while the X-rays were being taken, and, of course, while he got the blood samples, she concentrated on being brave.
Later, while Captain Thiel looked in her eyes with the bright little light, Mary said calmly, "Do you know my hypoalter, Susan Shorrs?"
The medicop drew back and made some notes on a pad before answering. "Why, yes. She's in here quite often too."
"Does she look like me?"
"Not much. She's a very nice little girl . . ." He hesitated, visibly fumbling.
Mary blurted. "Tell me truly, what's she like?"
Captain Thiel gave her his nice smile. "Well, I'll tell you a secret if you keep it to yourself."
"Oh, I promise."
He leaned over and whispered in her ear and she liked the clean odor of him. "She's not nearly as pretty as you are."
Mary wanted very badly to put her arms around him and hug him. Instead, wondering if Mrs. Harris, waiting outside, had heard, she drew back self-consciously and said, "Susan is the cause of all this trouble, the nasty little thing."
"Oh now!" the medicop exclaimed. "I don't think so. She's in troutle, too, you know."
"She still eats sauerkraut." Mary was defiant.
"But what's wrong with that?"
"You told her not to last year because it makes me sick on my shift. But it agrees in buckets with a little pig like her."