Not entirely sure, but from what I can see, Hokkyokusei is the name of the dojo, not a different style of Kendo... in essence, Kendo is Kendo, there aren't really different "styles", similar to Judo in that regard. The history is simply the history of Kendo.
No kanji to read but Hokuyoku generally means 'North Pole. There are some factional groups but generally Kendo is Zen Nippon Kendo Renmei sanctioned by Monbusho, the education authority. Gradings up to godanare prefectural. 6th Dan is a national level. Iaido Ryu belong to ZNKR, ZNIR (Zen Nippon Iaido) or ZIR (Zenkoku Iaido).
I googled it. The instructor Steve Voss was at the Kitamoto camp. That's the ZNKR seminar for foreigners doing Kendo. Seems up front. You have to be registered with the IKF, the foreigners section of ZNKR. The name is just the Dojo name.