Though the name is never directly used in the bible, it appeared in later retellings of the story of Joseph and is meant to be the wife of Joseph's employer "Potiphar" - the Captain of the Bodyguards to the Pharaoh of Egypt. The Egyptian's wife continually, though unsuccessfully, temps Joseph with seduction (Genesis 39:1-20). Then later in the Qur'an the same story is retold with different names (Chapter 12:21-35). 

The actual name "Zuleika" arrives in the middle ages from Persian epic poems and the Jewish stories of Sefer Hayashar which was first published in Venice in 1625. Zuleika's passion, in these expanded stories, herself a great beauty, leads to a suicidal state of depression. 
(A Coat of Many Cultures) 

All of this is very interesting, but the source of Sargent's title is more likely prompted by his very good friend, the humorist  Max Beerbohm whom was writing, around this time, his one and only novel by the name of "Zuleika Dobson".  

The title of Max's book was an obvious literary allusion to the old Persian poems. He sets his story, however, in contemporary times (1910's). Zuleika Dobson is an arresting beauty who visits her grandfather at Oxford who happens to be the Warden of Judas College. The minute she steps off the train, every undergraduate falls in love with her -- literally.  

Led by the very eligible and handsome Duke of Dorset, the entire class of under grads pledge their collective suicide as an extravagant gesture of their love for her -- hundreds of them -- and they do it. 

Believe it or not this book is a comedy, and I've even seen it listed (today) as one of the hundred greatest English novels. It's essentially a farce of Oxford life and nobility. The book was over thirteen years in the making and even though it didn't first go to print until 1911, John and Max were palling around London well before 1907 and certainly during that year. 

Elizabeth Oustinoff, in her chapter "The Critical Response" (Sargent Abroad) makes the point that this was probably an inside joke to Max. After all, the artist had to come up with hundreds of painting titles. With Max having drawn a number of humorous jabs at Sargent made public in caricatures; Sargent, has a chance to make a public nod back to his friend -- in a form that only Max would understand. That others would eventually get it -- but only later when the book was finally published -- would be the joke from Sargent.  
 

Notes: 
The obvious question, it seems to me, is how do we know Sargent's painting pre-dates the publication of the book since the painting is dated  "circa" 1907?  Richard Ormond answer this one for us in his essay "In the Alps: The Zuleika Pictures" (p.84, Sargent Abroad) Here, he tells us, a painting by that title had been exhibited in 1910 -- unfortunately he didn't say which exhibition. 

Often Sargent didn't title a painting until it either sold or was exhibited. If that's what happened in this case, it may have been less than a year before the publication of Max's book. If that's the case, the chances are even higher of Sargent knowing of Max's manuscript. 

See the Project Gutenberg's Zuleika Dobson by Max Beerbohm  

Exhibitions

Sargent in Italy, 2002-2003

• See the The Brooklyn Museum of Art 
• See more on Max Beerbohm
• See the year in review 1907