It would be best to start with examining the first occurrence of this designation as found in Isaiah 14:12. Here we find the name Lucifer is derived from Hebrew helel, literally, 'shinning one,' from the root halal, which means 'to flash forth light,' 'so shine,' 'to be brilliant.' The name helel, and its equivalent in related languages, was commonly applied to the planet Venus as a morning star because of its unrivaled brilliance. Venus is the brightest of all planets and at maximum brilliance shines shines more than seven times brighter than Sirius, brightest of all the fixed stars. When favorable situated, it is easily visible to the naked eye at noonday, and after dark it casts a shadow. The LXX renders helel as heosphoros, 'morning star,' literally, 'bringer of the dawn,' the common Greek designation when it appeared in the morning sky.
The name Lucifer comes from the Latin Vulgate, and means 'light bearer.' The term, as here used, seems first to have been identified with Satan by Tertullian, Jerome, and other early Fathers of the church, and came into common usage in this sense during the Middle Ages. In 2 Peter 1:19 Christ is referred to as phosphoros, 'day star'; literally, 'light bearer.' In Revelation 22:16 He is called 'the bright and morning star [literally, 'dawn star.' Or 'star of the dawn'].' As applied to Satan, the various terms—helel, heosphoros, Lucifer, etc.—seem to reflect the thought of the high position he once held in heaven , next to Christ, and to imply that he is even now, a rival of Christ. Strictly speaking, none of these terms is a proper name, though all have come to have that meaning; rather, they are attributive terms denoting the high state from which Lucifer fell. This description applies to Satan before his fall, as next to Christ in power and authority and head of the angelic hosts.
{SDA BBC, vol. 4, p. 170.}