No-Face symbolizes how children form an identity based on the people around them. Identity is one of the key themes of Spirited Away, most potently expressed in Chihiro losing her name to Yubaba, or Haku remembering he is really a water spirit. No-Face is very much like a small child in that he has no definite sense of identity and can communicate only in a limited verbal way. Like a child, he seems more motivated by urges and the need for affection than anything more sophisticated. And like a child, he is highly influenced by the adults and older children it encounters.
No-Face gives gold to other people in exchange for services because he does not seem to understand any other way of connecting with people. However, his usual method of persuasion does not work with Chihiro, who is not tempted by the same greed that fuels both her parents or the other spirits in the bathhouse. When No-Face reacts violently, it is not because he is evil. Rather, he is able to realize that the other workers are being greedy and so he consumes them, emulating their ravenous desire for profit. He almost takes on the identity of a greed spirit, devouring everyone and everything in sight until Chihiro purges him. Notice how the bathhouse workers were the reason for this sudden change: they display greedy behavior, and so No-Face emulates what he sees.
After this, No-Face returns to his previous form. He is more docile and helpless, once again like a child, and through Chihiro and Zeniba's positive influences, he is able to find his own identity as an apprentice to Zeniba. The fact that his talent his knitting and spinning is also significant in that this evokes a sense of No-Face creating an identity for himself, much like Chihiro does through her adventures in the spirit world.