This is one of the several species of Lyretail Damselfish in the genus Neopomacentrus.
It has a deep purple body with bright yellow in the tail and rear of the dorsal fin. It is from the western Pacific. It may be similar to a
young Yellow Lyretail, Neopomacentrus azysron, native to coral reefs of the Indo-West Pacific and growing to just over 7cm long,
but the tail streamers suggest it is an adult and the adult Yellow Lyretail has a full yellow tail (no purple edges) and yellow caudal peduncle.