Answer:
Rusty is indeed Firestar in the Warrior Cats, Rusty was Firestar's kittypet name in the very beginning in the series at book 1 Into the wild in The Prophecies begin. When he joined Thunderclan, Bluestar - the current leader of the clan - named him Firepaw for his flame-colored pelt. He eventually earned the name Fireheart for his loyalty, dedication, and a true heart. After Tigerclaw was banished from the clan, Fireheart became deputy and helped Bluestar lead the clan. When Bluestar's life came to an end, she said that he was the fire that would save the clan (a reference to a prophecy predicted by spottedleaf), and he ascended to become leader of Thunderclan, earning the name Firestar, and becoming one of the greatest leaders the five clans have ever seen.