Since so many people are mentioning Rin from Inuyasha, it's important to note two things: first of all, the actual name is pronounced "reen", while in most dubbed versions of Inuyasha they pronounce the name "ren" (like the name Ren). Secondly, in Inuyasha Rin's name is spelled with hirigana -‚è‚ñ- so it doesn't mean "cold", it actually has no meaning.

Pronounced "ṘEEN."

REEN sounds too snotty and it just hurts my ears. That's why I prefer pronouncing it RIN.