No, he intended it to be Eragon's.
Brom
Eragon becomes a dragonrider because his father Brom is one. But Eragon don't find out Brom's his father until The 3rd book.
Eragon first meets Brom in the town of Carvahall, where Eragon seeks his guidance after discovering a mysterious dragon egg. Brom becomes Eragon's mentor and teaches him about magic, dragon-riding, and the ways of the Dragon Riders.
Eragon's true father is Brom, a former Dragon Rider who becomes Eragon's mentor throughout the "Inheritance Cycle" series. It is revealed later in the series that Brom is Eragon's father, not Morzan as originally believed.
Yes Brom dies at the beginning of the 1st book by the razak and then eragon finds arya later
He tells Eragon that he was a dragon rider and he gives Eragon some wise advice. Well that guy says wise advice it probaly is but Brom aid some thing in the ancient language and tells Eragon to use it in an important situaition
Brom, Eragon, Saphira, Arya and the Ra'zac are a few of them.
Oromis
Eragon is Brom's son. Eragon and Murtagh are brothers through their mother Selena. Morzan is Murtagh's father, but Brom is Eragons so that makes Murtagh Eragon's half brother. It was revealed in the third book Brisingr that Eragon's real father is Brom, not Morzan as it was told in the second book Eldest.
Brom is only alive for a period of time in the first book, Eragon. He passes away after a fatal wound from the Shade he and Eragon fought. Eragon and Saphira built a tomb for him atop a mountain.
A red sword. It belonged to Morzan, Eragon's stepfather, and was won in a fight by Brom. Both Brom and Morzan are Dragon Riders. In the ancient language, it means "misery".