Why do you think Chris would have lied to Jim Gallien about his name and age?
At the time at which Christopher McCandless interacted with Jim Gallien, McCandless was still "hiding" from his family; he did not want to be found, especially by his parents, who he had managed to avoid for two years. While Gallien, who took McCandless to the Stampede Trail, clearly showed his generosity by taking McCandless so far and giving him food and his own waterproof boots, McCandless obviously felt that there was no need to return the favor by providing Gallien with anything other than a little bit of pocket change. At the point of their time together, McCandless was not yet ready to accept his real name and its connotations, and did not feel any obligation to provide information that might be used by his parents, should they manage to track him that far, or should Gallien decide to contact them on his own. Basically, McCandless had had nothing to do with his family for two years, and he was not about to allow someone else to make the choice to make it possible for them to reenter his life without his permission. However, it is important to note that McCandless signed his real name to his final note to the world, which he wrote shortly before his death; he had apparently made his peace with his identity and all that it signified.