The ethnonym and state name Russia(n) traces its origin back to older Rus’ (Русь). As the current standard etymology goes, this is thought to then derive, via the Varangian ruling class of pre-Slavic Russia, from Finnic *roocci ‘Sweden’, in derivatives ‘Swedish’; which is itself considered a loan ultimately from Germanic *rōþaz ‘rower’, in most versions via the name of the area of Roslagen on the eastern coast of Sweden, or perhaps various compound names in *rōþs- for its inhabitants. There are various details in this chain of hypotheses that are not exactly straightforward, and currently a lively session is ongoing at academia.edu, around a recent discussion paper by Viacheslav Kuleshov. 
Most discussion has focused only on the Scandinavian – Finnic – Slavic main chain. There are old offshoots also in other Uralic languages though, and on closer consideration I find interesting the existence of two separate groups of reflexes in Sami.
In this blog post’s title I’ve given the standard Northern Sami forms. The first of them is etymologically no trouble at all: it is simply a transparent loan from Old Finnish †Ruodzi /ruoθθi/ that probably does not need to be projected deeper back in Sami than the 17th century (around the time when the Swedish state itself, i.e. not just Swedish-affiliated Finnish peasants, begins to have a stable presence in the Northern Sami areas). Inari Sami ruátálâš ‘Swede’, Ruotâ ‘Sweden’ and Skolt Sami Ruõtˈt ~ Ruõcˈc ‘Sweden’ are transparently newer loans still. The first two come from spoken northern Finnish ruottalaine(n) ‘Swede’, Ruotti ‘Sweden’,  the last from standard Finnish Ruotsi. Lagercranz in Lappischer Wortschatz documents newer-looking loan variants from Northern Sami dialects too, e.g. (transposed to modern orthography) ruoha from Talma in Kiruna, ruohta from Gratangen and Nesseby, ruoha ~ ruohta from Parkalompolo in Pajala. I would take this variation similarly as evidence that there was no name of Sweden known even in Common Northern Sami (which very well might be older than a unified Kingdom of Sweden at all, putative Proto-NS seems to be closer to Proto-Samic than to modern NS dialects). Northern, Inari and (since WW2) Skolt Sami are of course also the three most Finnish-influenced Sami varieties. From Lule Sami on south I would presume ‘Sweden’, ‘Swede / Swedish’ to be instead direct loans from Swedish (Sverige, svensk). I have not checked primary lexicographic sources beyond drawing a blank for cognates of Ruoŧŧi in the Álgu database, but a quick look at Wikipedia incubators seems to confirm this, attesting Lule Sami gen.sg. Svieriga (nom.sg. Svierihka?), Pite Sami Sverji, Southern Sami Sveerje and Svïenske.
Explaining ruošˈša from Finnic is however harder. Already the sound correspondence *šš ~ *cc looks mysterious to me: all Sami languages would have the voiceless affricates c, č available (both plain and geminate, add preaspiration to taste), and substituting later Finnish *θθ as a palato-alveolar sibilant wouldn’t really make sense either. I have not found any real explanation or reference to one in the handbooks of Korhonen or Sammallahti. There seems to be at least one parallel though: Fi. viitsiä ~ NS višˈšat ‘to bother’. I could imagine this reflecting an intermediate early Finnish stage with a lamino-dental sibilant *s̪s̪, which is phonetically expected and perhaps directly ancestral to some of the small Finnish dialect areas with *cc > ss. There would be a better match if we assumed that the palatalization of Karelian čč was earlier found across Finnish as well (perhaps even as a retention: PF *cc after all comes from palatalized *ćć), and that assibilation took place already before any fronting, so that “very old Finnish” had a reflex *śś that could be adopted intact in Sami. But for this there is zero evidence across the Finnish dialect reflexes.
Kuleshov however has, in an earlier paper on the same topic, a promising suggestion that is new to me: borrowing not from Finnic but Slavic. This for starters fits the meaning better. Nowhere in Finnic does *Roocci mean ‘Russian’, and even the possible loan etymology into Slavic would seem to involve the semantic shift ‘Swedish’ > ‘Russian’ coming about within Slavic speakers. As an intermediate stage I would assume the word referring to Slavs affiliated with or ruled by still-Scandinavian Rus’. There is also common Permic *Roć ‘Russian’, usually analyzed as a loan from Finnic. I guess Permians should be predicted to follow roughly the same semantic trajectory as in Slavic however, once Scandinavian Rus’es cease to exist and are replaced by or assimilated into Slavs.
(Actually this also gets me wondering about Norwegians running trade connections to Old Perm via a northwestern oceanic route. They must have been known by some Permic name, and I wonder what… This is not required to have been the same as that for the inland Rus’, of course.)
Phonologically, NS uo from Slavic u does not immediately look good. Kuleshov’s suggestion is loaning already very early, before the Middle Slavic raising †ō > u. In this particular word this stage actually happens to be clearly attested even, in a Byzantine Greek translitteration Ῥῶς. On some thinking I have developed a different idea though. Any contacts with (pre-)Russians must have started at the eastern end of the Samic dialect continuum. And if we look at the other Sami varieties’ cognates of ruošˈša, we find not only identical Inari ruošˈša and roughly the same Skolt ruõšˈš, but also Kildin Sami rūšš. The correspondence “mainline” uo-a ~ Kildin ū is regular, probably regular enough that ū could be etymologically nativized back to uo, if the loan was transmitted thru Kildin or a similar Kola Sami variety (just as Rūʰt̀s = Rūʰcc for ‘Sweden’, mentioned by Kuleshov, must be etymologically nativized, either straight from Fi. Ruotsi or more likely from Skolt Ruõcˈc). This gives more flexibility in absolute chronology, which would be handy: the Middle Slavic era is usually dated somewhere in the mid 1st millennium, while the Russian Pomors arrive on the coasts of Kola peninsula a fair bit later, in the first centuries of the 2nd millennium. I do not think occasional reports of people further southeast by more trade-minded Norse or Karelians would be sufficient to establish a Sami name for the people who would eventually become Russians.
A different issue appears in the consonantism, but this too seems to work out by the assumption of borrowing initially into Kildin Sami. Samic palatoalveolar š from Slavic palatalized s’ is as expected; but why overlong *šš? In discussion Kuleshov has pointed out as a parallel the substitution of Russian medial с, ш as mostly geminate ss, šš even in recent loans into Finnic, a correspondence that is upon checking known to be fairly systematic but which I had not realized before. But so indeed: jorssi ‘ruff’, kassa ‘hair’, kassara ‘billhook’, kasseli ‘backpack’, kiisseli… Thinking a bit more, while this substitution looks unnecessary, it would be not so in varieties like Ludian or southern Karelian, where medial *-s- has been voiced to -z- or -ž- and the only native voiceless sibilants are therefore -ss-, -šš-. Browsing SSA, there are even cases with a geminate in the eastern languages but a singleton attested in Finnish, e.g. EFi. †kaasa (19th c.) ~ Krl. koašša etc. ‘porridge’; EFi. kosinkka ~ Krl. kossinkka ‘scarf’; EFi. ko(s)suli ~ Ingrian kossula ‘type of plough’; EFi. ku(s)sakka etc. ~ Krl. kuššakka ‘woven belt’. (However this pattern is weakened by forms kosinkka, kušakka even in southern Karelian, with singleton voiceless sibilants apparently re-established in loans.) Makes of course also a nice parallel to the long-running sound substitution strategy that Indo-European -p-, -t-, -k- are borrowed as Finnic -pp-, -tt-, -kk-, but -b-, -d-, -g- as -p-, -t-, -k-. This is by now regardless a strategy, a kind of a cousin of etymological nativization, and not a mechanical phonetic substitution.  I think this is also what allows the gemination pattern to turn up even in Russian loans into eastern Finnish, despite the availability of unvoiced -s-. Further in western and standard Finnish such loans have been of course mainly mediated by the eastern dialects.
Now what has this to do with a loanword into Sami? Directly nothing, I think: the Sami languages are not bound to Finnic and should be free to develop their own patterns of loanword adaptation. But in eastern Sami, from Skolt on, we also find medial voicing of sibilants, in the weak grade that is (the strong grade is a regular / “short” geminate, as everywhere in consonant-gradating Samic). This would have created the opportunity to innovate the same loanword nativization strategy: Russian -з- gets taken over as the paradigmatically voiced -ss- : -z-, versus Russian -с- as the consistently voiceless -sˈs- : -ss-. I have no data easily on hand on if this actually happens in Russian loanwords into Kildin Sami, but a draft paper by my colleague Markus Juutinen, on Russian loanwords into Skolt Sami, comes helpful. Some geminates from Russian -с- indeed turn up there: bie´sˈs ‘devil’ ← бес, [ki̮s̄sa̮] ‘bag made of sealskin’ ← киса, pleäsˈsjed ‘to dance’ ← плясать. All three must be fairly recent (note retained b-, pl- and lack of *ki > ǩi), but this is regardless evidence that the same adaptation-by-gemination strategy has been innovated in eastern Sami. Within a younger chronology, where rūšš is first loaned from Pomors in maybe the 12th century and perhaps reinforced as geminate during ongoing contacts, it does not seem outlandish to assume that medial voicing and also vowel raising to ū (IMO a part of an already Proto-Kola Sami chainshift) could have been in place already.
I do not know what to think of the absense of a known Ter Sami cognate of rūšš (we would predict rī̮šš = /rɨːɕː/). Is this merely a documentation gap? The main word for ‘Russia(n)’ in Ter Sami is however instead Tārra, cognate to the words for ‘Norwegian, Scandinavian’ elsewhere in Samic (NS dárru, etc.). While this is a neat parallel to the presumed Rus’ > Russian shift, it does raise questions. Were Pomors first interested in areas further north and west before showing much attention to the Ter Sami? Was there earlier an inland / coastal split within Kola Sami instead of the current west / east one?
A further interesting aspect of what this etymology adds up to is, I think, that although ruošˈša and ruoŧŧa still are likely doublets from a common ultimate source, their identical vocalism would be kind of accidental: the latter gets its uo straight from Finnish < Proto-Finnic *oo, the former develops thru Middle Slavic ō > (Old) Russian u → Kildin ū, which is only incidentally also < Common Samic uo. Under my current hypothesis, probably not even the shifts *ō > *ū in Slavic and Kola Sami can be considered connected: they merely reflect the universal tendency towards long vowel raising (besides, one is conditional, the other unconditional). Thus can typology of sound change conspire to create similar sound patterns via different routes. A kind of a second dimension to my earlier typology as parallel loanwords being somewhere between “diverging” (adopted in forms more different than they should be natively) or “converging” (adopted in forms more similar than they should be natively): they can also show correspondences “regular due to internal development” versus “regular due to unrelated developments”.
 Itself in response at a recent proposal that tries to sketch a novel Balto-Slavic origin for *Roocci; which I find so far still worse phonologically, semantically and sociolinguistically, so enough about that for this blogpost.
 Note also the Finnish second-syllable alternation between -a- in the ethnonym and -i- in the toponym, copied also in Inari Sami -á- ~ -â- (the latter with usual etymological nativization of stem vowels in F/S loans). This phenomenon remains without a clear known origin but is paralleled by Suomi ‘Finland’ : suomalainen ‘Finn’ and Lappi ‘Lapland’ : lappalainen ‘Lapp’ (≈ Sami). Presumably some two of these are analogous to the third, but I have no solid idea which way around. Slightly different is Häme ‘Tavastia’ : hämäläinen ‘Tavastian’ where the first seems to be a simple derivative in -e (within just Finnish we cannot tell very well if from *-eh or *-ek) from an earlier *Hämä.
 It has likely been originally phonetic though, way back when Proto-Norse and Proto-Germanic *-p-, *-t-, *-k- were still preaspirated or preglottalized. At least one example could show a similar development in an old loanword from Baltic: PF *rattas ‘wheel’ ← *ratHas < PIE *HrótHos.