The biggest reason people want fame is a lack of security, a lack of feeling content within themselves. Fame: what that means is we want somebody or some animal, creature to look at us. We want to be the centre of other people's lives, even if it just the dog. You walk up past the dog and you want the dog to look at you so that you become famous. That's all it is - a wanting for others to recognize me. Now if a person is content in themselves, if they feel quite secure within themselves, they don't need that, they just don't need it.
So insecurity is a root cause for wanting fame. How can we let go of it? Develop more contentment with who you are, develop more inner security. That all can come from a balanced practice.