The bull-running festival in Pamplona that Hemingway wrote about is the Festival of San Fermín, also known as Sanfermines. It is an annual celebration honoring Saint Fermín in Pamplona, Navarre, Spain.
The festival begins on July 6 with the chupinazo, a rocket fired from the town hall, and continues through July 14. Its most famous event is the encierro, held each morning from July 7 through July 14. Participants run ahead of six fighting bulls and accompanying steers along a route through the old city to the bullring.
Hemingway helped make San Fermín internationally famous through his 1926 novel The Sun Also Rises, originally published in some markets as Fiesta. He first visited Pamplona in 1923 and returned repeatedly. His writing emphasized the festival's energy, drinking, bullfighting, rivalries, and romantic tensions.
San Fermín is the festival's name; the running of the bulls is only one event within it. Pamplona Festival is an informal description, not the canonical name.