Murphy Cooper was the closest of Cooper's children. She had a drive to explore and discover the unknown, very much like her father.
Suffice it to say she did not like her name, as it had the connotation that she was the harbinger of bad luck. However Cooper reinforced the idea that her name is in reality a call to hope.
One morning, she claimed that her room was haunted by a "ghost", which was dismissed by both Cooper and Tom. Eventually, Cooper realized that it was important, as a series of rows of dust accumulated in a pattern consistent with binary, which led to the new headquarters facility for NASA. She became angry with her father upon his leaving Earth, taking it as him abandoning her, a grudge she holds for almost 25 years.
In her thirties, she worked with Professor Brand at NASA HQ, attempting to help him solve the problem of gravity. She discovered that Brand's gravity equation had inconsistencies that Brand did not believe were apparent. On his deathbed, it was revealed that Brand's gravity equation had been solved for years and that the entire "Plan A", to use gravity to save humanity on Earth, was a sham. She made this apparent to Amelia Brand in a message sent to the Endurance relayed via CASE and TARS.
Despite this revelation, Murph was still driven to save humanity, she felt that the solution lay in her old bedroom. Upon arrival at her old home, she was unable to convince Tom to leave, as the dust was causing respiratory issues with his family. She later drives out into the open field and burns a section of crop to cause a distraction for her to rescue her sister-in-law and her nephew.
While in her old room, she comes to the realization that her father was her ghost and that she was always being watched over by him, renewing her love for him. She discovered that the watch she was given by Cooper was twitching with Morse Code which read quantum data recovered by TARS inside the black hole which helped allow her discover a final solution to gravity to save the world.
Many decades later, Murphy was placed in hypersleep on her way to Cooper Station near Saturn to be reunited with her family as she became close to death, including her long lost father. When Cooper is finally reunited with her, she encourages him to seek out Brand instead of staying, stating that no parent should watch their child die.
In the original script, Murphy was the name of one of two Cooper's Sons.