What is the name of the battle in which Éomer defeats Saruman’s army in J.R.R. Tolkien’s The Lord of the Rings?

The battle in which Éomer helps defeat Saruman’s army in J.R.R. Tolkien’s The Lord of the Rings is the Battle of Helm’s Deep.

The battle takes place at the Hornburg, a fortress in the valley of Helm’s Deep. Saruman sends a large force of Uruk-hai and other servants to destroy Rohan’s resistance. King Théoden leads the defenders, while Aragorn, Legolas, and Gimli fight beside him.

In the book, Éomer has been imprisoned or excluded by Gríma Wormtongue’s influence, then arrives with Gandalf and a force of riders at dawn. Their arrival helps turn the battle in Rohan’s favor. The battle is also commonly called the Battle of the Hornburg, so that name refers to the same event rather than a separate conflict.