It's the first time I ever heard Reimu call Rinnosuke, "Kourin".

Canonically, only Marisa calls Rinnosuke with that name...hmmm..
..or nakatani just doesn't care.

But Reimu's calling him 霖之助... I'm sure that's 'Rinnosuke'..

Reimu refers to Rinnosuke as "Mr. Rinnosuke" according to Touhou Kourindou. (Man I always fail to remember the English sub-title.)

Sorry, mistranslation -_-
Guilty as charged...