After his amnesia, Talos requested that he be given a new name by the charr who found him. He did this because he felt that he was no longer the man named "Talos" and refused to let himself be called that name until he remembered who he was.
The reason the charr didn't kill him was because before the searing, the two of them were often running into eachother and constantly at a stale mate whenever they fought. They had a burning rivalry in battle because of this, and the charr wanted to finish what they started. But Talos, keeping his wisdom in tact, explained that he would not fight someone he couldn't remember, and promised to travel with the Charr warrior until he got his memories back. Then they could finish their fight.