You have to love all the different schools. We are Aikikai (AAA) but we have a kokikai Nidan who will stop by the dojo and sometimes show they way "they' do things. Our irimi nage is his kokyunage. We step thru uke center. So if my right arm is controlling the head, we would step through the center with our right leg. The kokikai version I was shown they do NOT step through and call it kokyu.
**sigh** Maybe it is better to not worry about names of technique after all.