A friend of mine, whose name is Raoni (he's brazilian, his name comes from a native root, also the tonic vowel is the very last [i]), started learning latin and I've been studying for a while. I started wondering after a while, how could one latinize his name or any name like his? Would it be * Raonius? * Raonis? How would it inflect?
My best guess is Raonīus
•Acc.: Raonīum
•Dat.: Raoniō
•Gen.: Raonīi
•Abl.: Raoniō
•Voc.: Raonīus (?) (Raonīe sounded too awkward for me)
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.
Do it to the best of your abilities and don't worry too much
Latinization would always be done to the best of one's abilities in the times where this was a thing.
Details varied according to what dialect one was most familiar with: spoken "vulgar" Latin vs. Church Latin vs. classic Latin vs. whatever some local variant.
Names often varied over the lifetime anyway. There was no such thing as "correct" or "wrong"; different styles would appeal to different communities, which weren't that coherent anyway because if the community in question was dispersed across Europe, linguistic details would vary anyway, even if both were supposedly using the same dialect.
Also, it was pretty normal to change the name over a lifetime; you're historically accurate if you prefer a different transliteration at a later age.
And that's how names like "Confucius" were created: Jesuits who ruthlessly latinized "Kǒng Fūzǐ" (see https://en.wikipedia.org/wiki/Confucius#Name). A much longer list of (mostly) genitives is at https://en.wikipedia.org/wiki/List_of_organisms_named_after_famous_people.
Another option to consider is if the name as a common meaning.
E.g. "Baker" became "Pistorius".
