Early in Daniel Quinn's Ishmael a great deal of focus is put on the name given to the gorilla character. When he is living in the zoo, the gorilla is given no name. during this time he also has relatively little ability to communicate. He is able to describe the conditions and issues of the zoo in retrospect, but is less aware and intelligent at the time. When he moves to the travelling circus he is given the name Goliath, and as he becomes aware of his name, he is essentially given new life as well. Goliath becomes his identity, although he does not fully identify with it's characteristics. With the identity a name has given him, Goliath is able to begin making his observations about humans, and their relative status to animals and the environment. he doesn't understand why he is an animal, or at least, why humans aren't considered animals as well. He also makes his first observations about humans relative captivity. He realizes that humans are imprisoned by expectations and requirements, if not by bars.
A further change comes in Goliath when he is visited by Mr Sokolow. Sokolow expects to see a beast, but realizes that Goliath's name does not fit, and renames him Ishmael. This is significant for a few reasons. First, it upends Ishmael's perception of himself. Second, it creates an important relationship between Ishmael and Mr. Sokolow. They will later become teacher and pupil, which is key in Ishmael's ability to communicate. Finally, it creates the identity of the primary teacher in this novel.
Ishmael is a name for someone with a divine purpose. This gives weight to Ishmael's argument, and can also be seen as an appeal to the reader to believe in the message being delivered. It also helps to give a broad analogy for the reader to follow. Ishmael was once the caged and ignorant Goliath. However, he was changed by a single interaction, and became both wise and free. This is the same path that the reader will see in Ishmael's student, as he is freed from his cultural prison and made to see the truth of his civilization.