"German iris" should only turn up bearded irises in a search, right? But a search for "flag" iris will turn up all kinds of irises (assuming it has been used for multiple species/cultivars, I haven't looked that close..). I just did a google search for "hanashobu" and all kinds of JI sites came up. As for "Celestial" I would skip that one.
You and Dee could choose to include hanashobu as a common name, it would be up to you guys. I like that word, myself. Maybe it would attract new members, perhaps from parts far away. A google search on that word would then bring up a link to ATP database... a good thing in my opinion.