Actually, his name may be Masaki Nakagaki after all. Check out this page:
http://www.wave-master.com/rdc/backnumber/146.html
WaveMaster is Sega's music studio so it's as official as you can get. On that page "Masaki Nakagaki" is credited for a "Pyramid Magic Medley". There's no kanji name to verify with, but seeing as his name is listed among other Phantasy Star related artists like Yutaka Minobe and Fumie Kumatani, that could very well be our guy.
And based on my dictionary, Masaki is a valid reading for 斉己.