It is common for male names to be put into the second declension when Latinized, in which case they inflect in general like any other second-declension noun. So going from Raonīus as a second-declension nominative form, it is quite clear that the accusative is Raonīum and the ablative/dative is Raonīō.
As far as I know, no native Latin name ends in -īus with a long vowel, so it might be a little hard to find analogies for the genitive and vocative. (Some names taken from foreign languages, most often Greek, end like this; e.g. Dārīus.). I think the usual pattern will most likely apply in this case, so the genitive will be Raonīī and the vocative Raonīe.
The declension of names ending in -ius with a short i show the following complications:
In the genitive singular, -ī can show up instead of -iī. The position of stress in contracted genitive forms ending in -ī is supposed to be the same as in uncontracted forms in -iī. It's not clear to me how this kind of contraction would even apply in the case of your friend's name, so I would just go with -īī. (The final vowel is long, although resources often don't mark that because it is fairly easy to predict once you know a little bit of Latin.)
Names ending in -ius in the nominative singular typically take -ī in the vocative. As in the genitive, the stress in -ī vocatives is supposed to be on the same syllable as in the nominative. However, vocative -ie also exists. Its distribution is a little tricky to describe, and is discussed in "O Egregie Grammatice: The Vocative Problems of Latin Words Ending in -ius", by Eleanor Dickey (2000). Since your proposal Raonīus ends in -īus and not -ius, I would recommend forming the vocative as Raonīe.