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Is there any open monosyllabic noun or proper noun in Russian?
If there is, what are the idiomatic suffixes for its adjective and appurtenance?
I know there are closed monosyllabic names and -ск/-овск often apply to them, such as Дон-донской, Днепр-днепровский.
Could -ск/-овск apply to open monosyllabic ones?
I'm asking this because I'm thinking if Rha, the Scythian name for the Volga, were transliterated into Russian (Ра) and had been an endonym, what would its adjective and appurtenance be?
Such nouns are extremely rare in Russian (in almost all cases that would be proper nouns, like family names derived from other languages, e.g. Ге (from French Gay), Хе (from Korean). I believe suffixation and derivation of adjectives is not possible from such nouns according to rules and structure of the Russian language (I least I can't think of any derivations from open monosyllabic proper nouns).
Native open monosyllabic nouns in Russian are indeed scarce, but a few do exist. These include зло "evil," тля "aphid," дно "floor, bottom of surface" and сто "hundred." In the case of зло, simply an -й is added to the stem in order to derive the adjective злой, and in the case of тля, the я transforms to е and the suffix -нный is added, тленный. Both дно and сто make use of metathesis + the suffix -(н)ый: сотый and донный, respectively. All of these words were originally disyllabic: zъlъ, tълja(?), dъno, sъto; and some might argue that they are still pronounced disyllabically today, i.e. тля /t.lʲæ/ and дно /d.no/, although they are supposed to be pronounced monosyllabically /tlʲæ/ and /dno/.
The loanword чмо "schmuck" (from Yiddish) derives its adjective by the suffix -шный: чмошный. However, the names of the letters of the Russian alphabet are indeclinable, and so are most open monosyllabic loanwords, for instance па "pas, step" (from French), го "Japanese boardgame" (from Japanese) and пи "pi" (from Greek). As far as I am aware these do not have any derived adjectives, and instead other constructions are used (for instance a genitive construction). The same is most likely true for the name you provided, Ра.
That puts to rest the monophthongal ones.
Meanwhile, I noticed I left out the diphthongal ones where the suffixation is much more viable, like the pattern of _ай - _айск
I also left out diphthongal monosyllabic nouns ending in -й in my post, as I considered them closed (i.e. phonologically /-j/). But such nouns generally derive their adjectives by the help of the suffix -ск- like you noted yourself, for example май > майский.