That was the summer of 1963, when everybody called me "Baby", and it didn't occur to me to mind.As I interpret that past-tense statement, she was not called "Baby" after that summer. In the fall, she began attending Mount Holyoke, a woman's college located in South Hadley, Massachusetts. In the fall, she moved from her home into a college dormitory.
It's unlikely that the Houseman family lived in or near South Hadley, enabling Baby to live at home while attending college. Dr. Houseman had been the doctor of Max Kellerman, the owner of the resort in the Catskills Mountains, so the Houseman family and the Kellerman had lived in the same vicinity at some time. It's much more likely that the two families had lived in the vicinity of New York city (population 8 million) than in the vicinity of South Hadley (population 17,000).
During the opening scene inside the car, we see that the Houseman family is driving on Highway 87, which goes north from New York City. If the family lived in Massachusetts, they would have driven on Highway 87 very briefly or not at all.
As long as Baby lived in the Houseman home, all her relatives and friends -- everybody -- called her "Baby". When she moved far away to the college dormitory, she would be able to rid herself of that nickname.
I myself have a cousin whose birth name was "Albert", but all his immediate and extended family -- including cousins such as myself -- always called him "Pogie". Even though we all are more than 60 years old, I still think of him only as "Pogie" and use only that name when I discuss him in family conversations. However, everyone who came to know him after he went away to college knows him only as "Albert".
Before the movie's story began, the song was "By My Baby". Immediately after the story began, the song was "Big Girls Don't Cry". The story is about the protagonist's transition from being a pre-story "baby" to being a post-story "big girl".
Later in the story, the protagonist's birth name is revealed (at 1:40 in the video clip):
Johnny: What's your real name, Baby?
Baby: Frances, for the first woman in the Cabinet.
Johnny: Frances. That's a real grownup name.
The "first woman in the cabinet" was Frances Perkins, who was the Secretary of Labor from 1933 to 1945 -- through the entire presidency of Franklin Delano Roosevelt. Perkins graduated from Mount Holyoke College in 1902.
The Houseman's choice of this name for their daughter indicates that the parents -- Jake and Marge Houseman -- were liberal Democrats.
It's likely that the screenwriter Eleanor Bergstein was named after FDR's First Lady Eleanor Roosevelt.
Eleanor Bergstein's real-life older sister is named Frances.
The father's name is Jake -- short for Jacob, the name of a Jewish patriarch. (The father in Eleanor Bergstein's first movie, It's My Turn, is likewise named Jacob.)
The mother's name is Marjorie, a variant of the English name Margaret, from the Latin word for "pearl".
We can suppose that the father grew up in a rather Jewish family and that the mother grew up in a secular-Jewish or even Gentile family.
The oldest daughter's name is Lisa, short for Elizabeth, originally from the Hebrew name Elisheba, which means something like "God's Promise".
The youngest daughter's name is Frances, which is a Latin "baby name" meaning "free". For some reason, the name was disliked by girls in the middle of the 1900s. Frances was the name given at birth but soon rejected by the famous actresses Judy Garland, Dinah Shore and Dale Evans.
The oldest Houseman daughter, Elizabeth, grew up to become a doctor's housewife, and the youngest daughter Frances grew up to become a politician.
After the youngest daughter Frances was born, the Houseman parents decided that she would be their final child. Frances would forever stay "the baby of the family", which is why that nickname stuck to her.
The mother did not want to spend her entire adult life raising children. She wanted to raise only two children and then devote herself to a career working outside the home.
Lily Rotherman, writing for Time magazine, has claimed that the protagonist originally was supposed to have the birth name Jacqueline.
.... the real inspiration for the Dirty Dancing story may be someone who only appears in one moment in the movie — during the credits, as a special thanks. Her name is Jackie Horner and, according to interviews conducted by the writer Sue Tabashnik for her book The Fans’ Love Story, her life provided much of the plot. Horner, who spent summers at Grossinger’s Hotel and later worked there as a dance pro, consulted with Bergstein in 1985, prior to filming.If that is true, then I speculate that Bergstein changed the name from Jacqueline (Jackie), because that name would have been associated confusingly with Jacqueline Kennedy.