In Latin there is only one type of R and as far as I know the combination RH does not appear in native Latin words. The corresponding Greek letter rho can have two kinds of breathing (rough ῥ, smooth ῤ). When a word (incl. name) is transliterated from Latin to Greek, which rho is used? Is it always smooth? I assume smooth is closer to the pronunciation in Latin.
First, a pretty banal orthographic point. In Greek, only initial rho has a breathing mark, and there are only two recorded words (ῤάρος and its diminutive ῤάριον) that use a smooth breathing. Though it's not entirely clear why these words have a smooth breathing, they are obviously anomalies.
The above strongly suggests that smooth rho wouldn't have been used to transcribe Latin words beginning with "r." It becomes even more convincing if we introduce the most basic of counterexamples: "Roma": Ῥώμη (= Rhōmē).