Obscurity is being insignificant or unknown, not noticed. If people are attached to obscurity they don't want to be in the limelight because they are afraid of fame. They don't want to be noticed, because they may be afraid of being blamed, or afraid of the responsibilities that come with fame. Obscurity is a very good word for the opposite of fame. Some people have a craving for obscurity when things are difficult, or they feel a lack of confidence about what they've done. I can't really think of any other suitable opposite word to fame except this. Fame is where you are out in the front, or you get the attention of other people. Some people don't want the attention, even to the point that they will withdraw completely, so that people don't notice them. Sometimes this comes from a lack of confidence in themselves as well.