The phrase 'dragon of the rain' may be translated as雨ã®ç«œ (ame no ryuu) in Japanese.
The Japanese word for Dragon is "Ryuu"
Doragonfurūtsu
ドラゴンストライキ
Kagami Ryū
ginryu
'Kinzoku no ryuu'.
ryu no ha
ryu-ken
Doragon iki
to say dragon in Japanese is 龍 and it is read ryuu hope this helps :)
shinnu ame
'Small dragon' would be 小さい竜 (chiisai ryuu) in Japanese.