My mother is from County Cork,
Ireland, and she says, "ROH-nun." That's what my brother would have been called had he (we) been born there. When said with the soft Gaelic "r" it's so handsome.
Sometimes different parts of
Ireland pronounce names / words differently. So I can't say for sure this is how the entire country says it. For what it's worth, I live in the U.S. and I'd say, "ROH-nun" too.