First it is best to understand the term "psyche." It is defined below.
…the psyche…refers to the forces in an individual that influence thought, behavior and personality.
In Truman Capote's "Miriam," aspects of Mrs. Miller's repressed psyche might be seen in the physical details of the young Miriam, as well as the child's independent—even forceful—nature.
When the child is first introduced, several details are noted regarding how she looks. These observations are more meaningful if the reader studies Mrs. Miller first:
The other people in the house never seemed to notice her: her clothes were matter-of-fact, her hair iron-gray, clipped and casually waved; she did not use cosmetics, her features were plain and inconspicuous, and on her last birthday she was sixty-one. Her activities were seldom spontaneous: she kept the two rooms immaculate, smoked an occasional cigarette, prepared her own meals, and tended a canary.
Mrs. Miller does not make an impression. There is nothing beautiful about her appearance—she wears no make-up, has short grey hair and is very plain. Her clothes are subdued—perhaps business-like and/or "serviceable."
By comparison, the young Miriam has very unusual hair:
Her hair was the longest and strangest Mrs. Miller had ever seen: absolutely silver-white, like an albino’s.
The child has a graceful, sophisticated "bearing" (or manner of moving).
There was a simple, special elegance in the way she stood...
While Mrs. Miller may dress in functional clothing, young Miriam wears a dress and chain of subtle style:
Her dress underneath was prim and dark blue. A gold chain dangled about her neck...
When Mrs. Miller next sees Miriam, she is dressed in silk, even though it is the middle of the winter. The dress is white with a beautiful cut, and makes a gentle sound as she walks, inferring elegance and a "presence:" the ability to move the air—even the world around her—as she walks. The beret she enters wearing might also give her a jaunty or sophisticated manner.
She dropped her coat and beret on a chair. She was indeed wearing a silk dress. White silk. White silk in February. The skirt was beautifully pleated and the sleeves long; it made a faint rustle as she strolled about the room.
Young Miriam studies an artificial flower:
"Imitation," she commented wanly. "How sad. Aren’t imitations sad?" She seated herself on the sofa, daintily spreading her skirt.
The inference is clear as the story progresses: not that young Miriam is an imitation, but more likely that Mrs. Miller is an imitation of the young woman she once was.
The elements of Mrs. Miller's repressed psyche might include a desire to be young and beautiful, to wear lovely clothes, to have long and lustrous hair again, to make people take notice of her in a room, to have the confidence the young often exude, the ability to make decisions that others notice—and most importantly, that she be connected to other people as we could assume she was when she was younger, and before her husband died.
The biggest problem with the young Miriam is that she is robbing Mrs. Miller of her identity, her sense of independence and any connection she might have to the world. As Mrs. Miller seems to lose control of her life—being dominated by young Miriam—we might assume that the personality, ideas, and behaviors of Miriam Miller simply disappear one day—totally repressed in the presence of the stronger Miriam—seemingly Mrs. Miller's doppelganger.