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Japanese morning glory (here kengyūka, but more usually asagao) is taxonomically Ipomoea nil.
For the different varietals listed on the same page:
Shukkon
I can't make out what "shukkon" is supposed to mean, in this context -- though it is clear that it refers to a particular colour of morning glory (in shades from a pale violet to light blue colour -- use Google image search for "宿根朝顔" to see what they look like) . The original text in the raws has「宿根朝顔だってさ」(shukkon asagao datte sa), but the only entry I can find for 宿根 is "(Buddh) fate predetermined from a prior existence".
Heavenly Blue
"Heavenly Blue" is given in katakana-transcribed English (ヘブンリー・ブルー). It seems to be a fairly recent varietal, hence the English name. Very pretty sky-blue colour.
Yaguruma
"Yaguruma" (矢車), or arrow wheel, is the name of the windmill wheel sometimes found on top of the poles on which carp streamers (windsocks) are raised (use Google image search for "矢車" to see what they look like). The comparison with the white-striped varietal of morning glory (Google image search : "矢車 朝顔") is obvious.