Some types of Buddhism do believe in the ability to keep your personal identity or ‘self’ after death. Mahayanic Buddhism believes that once a person achieves enlightenment they can make a choice at the moment of death. They can either return to the universe and become one with it (not be reborn at all) or they can choose to return in order to help others to achieve enlightenment. These buddhas (enlightened ones) who choose to return are known as BODHISATTVA. They retain full memory of their past lives and live again as enlightened beings, or buddha. The Dali Lama, in Tibetan Buddhism, is an example of bodhisattva.
Thus, not all Buddhists believe the same thing and these Buddhists will have to face PHILOSOPHICAL QUESTIONS about the existence of the soul as a separate substance – see Dualism and Materialism!