Bearing this name, I wanted to let the world know how many times it has been pronounced wrongly. Especially English-speaking people seem to have great difficulties with the way it is pronounced: a rolling /r/ and a soft /g/.
I was told my name had two possible translations: "brave warrior" and "advisor in the battle". It would indeed come from anything that has to do with 'reign' (possibly Reinhild) but is also related to the male Ragnar, who is a mythological Scandinavian figure (as far as I know).
I was born in Sweden and came to America when I was 6 years old. Americans can not pronounce my name correctly. I don't bother to tell them the correct pronunciation unless they ask and are truly interested. So I tell them it sounds as if it is spelled Rahng-nah and the R is slightly rolled.