In the story, the protagonist, John McClane, is a New York cop who gets caught up in a hostage situation at the Nakatomi Plaza in Los Angeles.
The story's working title was "Die Hard," which caught the attention of the filmmakers, who saw it as a fitting description for the film's action-packed, thrilling nature.
So, while the title "Die Hard" doesn't directly come from the movie itself, it was inspired by the short story that the movie is based on.