The word "soviet" (сове́т) means "council" or "advice." So one translation of Союз Советских Социалистических Республик could be "Union of Socialist Council Republics" or - at a stretch -"Union of Wise Socialist Republics". What do we know of any deliberate choices made by English speaking press and governments to adopt "Soviet" in its untranslated form as part of the English translation? I can't think of any other countries whose names are only partially translated into English like the USSR.
Languages do naturally and regularly take on words from other nations/languages. The obvious other example in this context would be the Italian word fascism which became an internationally accepted term for the far right movement mainly because Italy "got there" first.
Soviets, when they were first created in Russia in the 1905 uprising, were really federations of strike committees who had taken over the functions of government in an area/city (so slightly more specific than just a council) and came to become the name for the organisations that ran what was to become the USSR after the 1917 revolution (even though their original shape or content soon disappeared, but the title persisted).
So the word Soviet was well established internationally by 1923 when the USSR adopted that name and was shorthand for the kind of workers' revolutionary government that briefly sprang up across Europe at the end of the First World War. As such the word conveys something far more specific, or politically loaded, than perhaps the driest translations from the Russian would give us - nor was it a particularly unfamiliar term when the USSR got its name.
The word was common enough outside of Russia that when other areas had similar uprisings they too would often call themselves by this Russian term, just as when Oswald Mosley set up his political party in the thirties he called it the "British Union of Fascists" despite the F in BUF being an Italian term - precisely because they saw themselves as part of international movements and so international terms would often (although not always) come naturally to them.
Donny Gluckstein's book "The Western Soviets" is a good overview of the range of places in Europe that adopted the term Soviet after workers' uprisings. This includes English speaking places like Limerick in Ireland who set up a "Soviet" in 1919 at the start of the Irish War of Independence.
In this sense Soviet had become an English word (as well as a French, German, Italian, etc word) with specific historical and political connotations that "council" simply does not convey.