In J.R.R. Tolkien’s The Lord of the Rings, the horse given to Aragorn by Éomer is Hasufel.
Aragorn meets Éomer and the Riders of Rohan while searching for Merry and Pippin. Éomer has been ordered away from Edoras after defying the influence of Gríma Wormtongue, but he still recognizes Aragorn, Legolas, and Gimli as allies. He lends Aragorn the horse Hasufel, while Legolas receives Arod.
The names are easy to mix up because both horses help the companions travel across Rohan. Hasufel is the horse associated with Aragorn during this part of the story. Brego is Théoden’s horse, while Shadowfax is the exceptional horse later ridden by Gandalf. In the film adaptations, horse details and scenes are presented somewhat differently, so the answer depends specifically on Tolkien’s written narrative.