Question: What was Darcy's estate called in Pride and Prejudice?

Pemberley


Pemberley is the fictional country estate owned by Fitzwilliam Darcy, the male protagonist in Jane Austen's novel Pride and Prejudice. It is located near the fictional town of Lambton, and believed by some to be based on Chatsworth House,[1] near Bakewell in Derbyshire.
In describing the estate, Austen uses uncharacteristically explicit symbolism to represent the geographical home of the man at the centre of the novel. On first visiting the estate, Elizabeth Bennet is charmed by the beauty of the surrounding countryside, as indeed she is by Mr. Darcy himself. Elizabeth had already rejected Mr. Darcy's first proposal by the time she visits Pemberley—it is his letter, the praise of his housekeeper, and his own courteous behaviour at Pemberley that bring about a change in her opinion of Mr. Darcy.
In Pride and Prejudice

They gradually ascended for half a mile, and then found themselves at the top of a considerable eminence, where the wood ceased, and the eye was instantly caught by Pemberley House, situated on the opposite side of a valley, into which the road with some abruptness wound. It was a large, handsome, stone building, standing well on rising ground, and backed by a ridge of high woody hills;—and in front, a stream of some natural importance was swelled into greater, but without any artificial appearance. Its banks were neither formal, nor falsely adorned. Elizabeth was delighted. She had never seen a place where nature had done more, or where natural beauty had been so little counteracted by an awkward taste. They were all of them warm in their admiration; and at that moment she felt that to be mistress of Pemberley might be something![2]
 Jane Austen (1813).

In other media
Renishaw Hall, Derbyshire, England, UK was the setting for Pemberley in the 1980 BBC adaptation of Pride and Prejudice starring Elizabeth Garvie and David Rintoul, adapted from the novel by Fay Weldon.
Lyme Park, near Stockport, was the setting for Pemberley for the 1995 television series of Pride and Prejudice starring Jennifer Ehle and Colin Firth.
Chatsworth House, the original inspiration for Pemberley, was used for the exterior scenes for Joe Wright's 2005 film version of Pride and Prejudice starring Keira Knightley and Matthew Macfadyen. However, Wilton House was used for many of the interior scenes, such as those featuring Georgiana Darcy. Jane Austen mentions Chatsworth in the novel as one of the great houses Elizabeth and her aunt and uncle visited before Pemberley during their visit north. The Duchess of Devonshire believes that the author was thinking of Chatsworth House when describing Pemberley due to the great number of similarities between Chatsworth and Pemberley. Chatsworth was again used for exterior, and some interior, scenes for the BBC adaptation of Death Comes to Pemberley.[3]
Harewood House, near Leeds in West Yorkshire, was the setting for Pemberley in the ITV fantasy series Lost in Austen. This series was not a direct adaptation of the novel, but the novel provided the majority of the plots, characters and inspiration. Some interior scenes in the BBC adaptation of Death Comes to Pemberley were filmed at Harewood.
Pemberley Press is the name of the publishing house that Bridget Jones works at in the 2001 film Bridget Jones's Diary, in homage to Pride and Prejudice.
In The Lizzie Bennet Diaries, a vlog-style modern adaptation of Pride and Prejudice, Pemberley Digital is the name of Darcy's company. Darcy says Pemberley is the name of the place that his father's family comes from in England.

Renishaw Hall as Pemberley in the 1980 TV serial
Lyme Park as Pemberley in the 1995 TV serial
Chatsworth House as Pemberley in the 2005 film
Harewood House as Pemberley in Lost in Austen