As Mike says, no IJN alpha-numeric designation, Shi (experimental) number, or Kōki (imperial year) model number appears to have been assigned to the Kikka, but I think there was an additional designation for the aircraft: Kōkoku Nigō Heiki (皇国二号兵器), meaning, "Imperial No.2 Weapon."
I’m on the way to bed and can’t put my hand on a source for this, other than my notes on the aircraft, but I think that information comes from Famous Aircraft of the World no.76: Japanese Army Experimental Fighters, Tokyo: Bunrin-Do, August 1976.
Don