I'm from Glasgow and I know several Ruaridhs, but every single one of them spells it a different way. If you look on the registry office's website you'll see how many variations there are. If you counted them all up it'd be in the top hundred names, easily. I presume only one of the spellings is actually correct (yours?).
I've always seen the Irish version spelled Ruairi with a fada above the first i. Is that not correct?