My question is did Lucifer have another name when he was in Heaven before he got kicked out?

Answer:
He has different names in scripture like Beelzebub, Abbadon, Apollyon.

In Ezekiel Lucifer was referred to as the anointed cherub before his fall.

Ezekiel 28:13-14  Thou hast been in Eden the garden of God; every precious stone was thy covering, the sardius, topaz, and the diamond, the beryl, the onyx, and the jasper, the sapphire, the emerald, and the carbuncle, and gold: the workmanship of thy tabrets and of thy pipes was prepared in thee in the day that thou wast created.  Thou art the anointed cherub that covereth; and I have set thee so: thou wast upon the holy mountain of God; thou hast walked up and down in the midst of the stones of fire.

Good question,
Pastor Brad