The fortress defended at the Battle of Helm’s Deep in Peter Jackson’s The Two Towers is the Hornburg.
The Hornburg is part of the larger defensive complex known as Helm’s Deep in the kingdom of Rohan. In the film, King Théoden leads civilians and warriors there while Saruman’s Uruk-hai army advances under the command of the high-ranking captain Gothmog.
The extended battle sequence is one of the trilogy’s major set pieces. Aragorn, Legolas, and Gimli help defend the fortress, while Gandalf later arrives with reinforcements led by Éomer.
Helm’s Deep and the Hornburg are related but are not exactly interchangeable names. Helm’s Deep refers to the valley and defensive area, while the Hornburg is the fortress itself. This distinction makes the fortress name the more precise answer.