Eragon touches the dragon, leaving a silver mark on his palm. He is now a Rider. He then sneaks the dragon some food. Next morning he builds a small hut in the trees for the dragon, to keep it safe from predators. Over the next month, he raises the dragon in secret, speaking to and teaching it and discovering their mental connection. As it grows bigger, he builds a hut on the ground, that is much larger than the first one he had made in the tree. The dragon grows quickly, and eventually he decides to show it to Garrow and Roran, but returns to Carvahall first to ask Brom about dragons and Riders, and to give his dragon a name. Before he leaves, he hears his dragon's thoughts saying his name.
For the first time he did not think of the dragon as an animal. It was something else, something... different. He raced home, trying to escape the dragon. My dragon.— Final words of Awakening