Finnish Reds (who did not have the chance to rename themselves Communist for the simple reason of being busy losing war when umbrella party RSDLP(b) renamed itself)
IMHO the Finnish Social Democratic Party did not consider the Russian SDLP as its umbrella organisation, as the SDP was, more or less, a homegrown group, modelled after the German Social Democrats. There were links to the Russians, but they were more personal than organisational, Lenin and the Rahja brothers being a case in point.
You have to remember, that the Finnish political scene was quite detached from Russian politics already during the autonomy. The SDP never went as far left as the Bolsheviks: even when the constitution of Red Finland was adopted in February 1918, it was mostly based on the US and Swiss constitutions. Those Finnish emigrants, who moved to Russia after 1918 were mostly from the left fringe of the party, and being now dependent on the Bolsheviks, it was natural they would call their
splinter group "the Finnish Communist Party".
So I think it is not a bygone conclusion, that in a "Reds Victorious" Finland the party, with a moderate majority, would have been called "Communist", though with the links with Lenin and pals becoming stronger after 1918 it could have happened.
...several important and less important butterfles. Swedish neutrality will be butterflied away almost certainly. They'll probably join Axis. I don't see many significant consequences of them doing htis, as general consensus tells us that they did everything Nazis wanted them to do short of direct participation and sending their (and Danish) Jews to camps. Although no Bofors AA guns for the RN and USN could mean some extra trouble for Allies.
Another butterfly could be... survival of the USSR. This is a bit of long shot, but I suspect that Finnish Worker's Republic will not join USSR (although they will be satellite state for all intents and purposes), as it wasn't integral part of the Russian Empire. Instead, it could be part of the Soviet "Sphere of influence", together with Mongolia and Tuva OTL. This will, in turn, increase chances of Lithuania, Latvia, Estonia not becoming parts of the Soviet Union in 1940, as Stalin will be more reseptive to "together but separate" idea.
I agree that Finland might have retained her independence, at least on paper, for some time. But I think incorporation into the USSR would have happened sooner or later, say, in the late twenties.
Red victory in Finland might lead into one or all of the Baltic states being incorporated into the Soviet Union even before the twenties. In OTL, the Finnish (White) government supported Estonian independence and troops were sent to help out: it is plausible, that in case of Red victory Finland could have similarly been used as a power base to help the Red Army in Estonia. After substantial Russian help against the Whites, Finland would have been in no position to refuse to help in the Baltic area.
There is the possibility that the Red victory in Finland, and the possible consequent success in the Baltic states could have been seen as supporting the idea of "exporting revolution" among Bolshevik leaders. It could have strengthened the internationalist viewpoint and butterflied away the "Socialism in one country" thesis. The result, a Soviet Union more aggressively seeking world revolution?