Is there a proper name that [name]Baby[/name] is a nickname for?
Maybe [name]Barbara[/name] or another name starting with B.
My brain can’t get passed “Dirty Dancing”
Her name was [name]Frances[/name]…
nameberry says it’s a “form of [name]Babe[/name]” and [name]Babe[/name] is a nickname for [name]Barbara[/name]. Also listed is [name]Bebe[/name], which links to [name]Beatrice[/name] as a nickname (which makes sense - [name]Bea[/name], [name]Bebe[/name]). I think [name]Bebe[/name] in more of a Spanish ‘b”b”’ is how people have been saying ‘baby’ lately when talking about their baby or babies in general.
Now that you mention in ‘Dirty Dancing’ that her name was [name]Frances[/name], my first idea was actually that if someone is called ‘[name]Baby[/name]’ as an adult, perhaps they were known as ‘[name]Baby[/name] [Name],’ like “[name]Baby[/name] [name]Frances[/name]” as a child and instead of becoming [name]Frances[/name], they were just called [name]Baby[/name] - or even never called their name. If you call your kid “the baby” more often than their name, it may rub off as a permanent nickname.
I actually got the idea from dirty dancing then it just sort of grew on me… I think it’s cute:)
I feel a quote coming on: “Nobody puts [name]Baby[/name] in a corner.” 
Uh oh…here comes the song now: “Now I’ve had the time of my li-i-ife, and I owe it all to yo-oo-oo-oo-ou…”
It’s a good connotation though! [name]Don[/name]'t you think?
Here is another one for everyone, [name]Nena[/name]: where does that come from?
I’m half asleep, but I just wanted to quickly say that I love the movie “Dirty Dancing,” and was simply taking a walk down Memory [name]Lane[/name] with the quote and the song.
(I wasn’t making fun of the [name]Baby[/name] nickname.) 
I think [name]Baby[/name] is sweet, but then again, it may be viewed as a derogatory or condescending term by some when used on an adult, along the lines of calling a woman “[name]Babe[/name].”
Best wishes to you!
(Off to bed I go!)
All I could really find is [name]Beatrice[/name]/Breatrix or [name]Barbara[/name]. [name]Baby[/name] could be spelled [name]Bebe[/name] or [name]Bibi[/name] and then that opens the door as being a nn for pretty much all “B” names.
I found [name]Bibi[/name] to be a nickname for [name]Brittany[/name].
[name]Nena[/name] hmmmm right off I can think of Nenet - Egyptian which means goddess of the deep.
nameberry says, [name]Nena[/name] is a variation of [name]Nina[/name]. [name]Nina[/name] is a diminutive of [name]Antonina[/name].
https://nameberry.com/babyname/[name]Nena[/name]
https://nameberry.com/babyname/girl/[name]Nina[/name]