Translation:She has a daughter whose name is Maria.
Names typically aren’t translated unless they are the Pope, a saint, an important historical figure, or occasionally current monarchs. Or if they’re fictional. So unless it’s the Virgin Mary or Mary Queen of Scots, you’re better off leaving it as “Maria.” But if you really want to translate it as “Mary” here, it’s possible (at least for this sentence). I changed the default translation to “Maria,” but left in “Mary” as an option.
I really hate that! In Guy de Maupassant the English translation reads, she was called "La Fleur de la Ville" which makes no sense to many English only speakers. The truth of what he saying is this girl was SO beautiful the people of the village called her "The Flower of the Village" which is actually MEANINGFUL. I know it is proper translation technique not to translate names, but SOMETIMES that is just plain WRONG!!!! Rant over.
For literary translations, it depends a lot on the translator and the type of text whether characters' names are translated. Trends change over time as well. In books you'll see a range, even some cases where they have a weird mix of names in both languages because some were translatable and some not. I'm not familiar with the text you're referring to, but if it's a nickname and not an actual name, I'm a little surprised it wasn't translated. I'm sure the translator had his or her reasons, though.
Il cui is actually referring to nome. Let's put it in this way:
Lei ha una figlia. Il suo nome è Maria.
She has a daughter. Her name is Maria.
Lei ha una figlia il cui/il quale NOME è Maria. Otherwise it wouldn't be "il" but "la quale/la cui" since "figlia" is feminine.
Hope it's all clear
I would love to know more about the use of "il cui" – could you use it for other cases where you'd use "whose BLANK IS"? Could I say "Ho un dottoressa i cui cappelli sono rossi" = I have a doctor whose hair is red? or Mia amica ha un fidanzato la cui lasagna è fantastico!=My friend has a boyfriend whose lasagna is fantastic Are these correct?
- Ho una dottoressa i cui capelli sono rossi
- La mia amica ha un fidanzato la cui lasagna è fantastica
But it's a bit formal, in informal conversation it's more likely to hear
- Ho una dottoressa dai capelli rossi
- La mia amica ha un fidanzato che fa una lasagna fantastica
- Lei ha una figlia di nome Maria
Then again, some of these uses of da and di can be more complicated to learn.
"Di chi" means "whose" in a question, not as a relative clause. Since this isn't a question, you need to use "il cui." So you could say:
Di chi è questo libro? Whose book is this? (question)
Di chi sono questi fiori? Whose are these flowers? (question)
It can also be an indirect question, but still asking to whom something belongs:
Non so di chi è. I don't know whose it is. (indirect question)
With "il/la/i/le cui," on the other hand, we are using these to tie part of the sentence to the person it belongs to rather than asking who owns it. So we could say:
La donna, il cui gatto vedi nella foto, è una mia amica. The woman, whose cat you see in the photo, is a friend of mine. ("Il cui" ties together "woman" and "cat.")