Is Lucifer Satan's angelic name?
Yes. Reference is made to Lucifer when he was ousted out of heaven when he pridefully rebelled against God.
"How art thou fallen from heaven, O Lucifer, son of the morning! How art thou cut down to the ground, which didst weaken the nations!" (Isaiah 14:12 KJV)
"And He [Jesus] said to them, "I saw Satan fall like lightning from heaven" (Luke 10:18).