I found that the Third International sponsored a worldwide transformation of former “socialist” parties (that was concretely related to the rejection of so-called “reformism”, to be somewhat upgraded to a more revolutionary stance, aiming to the “proletariat dictatorship”), who were thus prompted to become “communist” even in their names.
Why did not the same idea apply to the USSR, that always kept its “socialist” definition?
The reason is that there are two different concepts that are named "communism". One is the final stage in the Marxist(-Leninist?) development model (after archaic/primitive classless societies, slave-holder societies, feudal societies, capitalistic societies and socialist societies) It is marked by (again!) a classless society, a total worker's paradise etc. As far as I am aware the Soviet Union and its satellites never claimed to have reached that stage of development. They were still in the transition between Capitalism and Communism, i.e. in the Socialist phase of development.
The other concept is the political movement that works towards the establishment of "Communism, the development stage".
It is always fine to name a party after a political movement. And in fact many of the ruling parties in the Soviet bloc called themselves "communist". E.g. the CPSU.
But naming a country after some distant of what it wants to be would invite misunderstandings and derision ("Why can I not have what I want? Marx said 'everyone according to his needs'!)
It is good to know that by Lenin's stance USSR was not in fact a socialist state. Their aim was socialism and eventually communism (in modern parlance people think of socialism and communism, usually communism is just though of a subcategory of socialist views. In fact Marx himself used communism and socialism interchangeably as an economic mode), but at Lenin's time they were not even an industrial country. In fact Russia was in the verge of collapse after the WW1, civil war, economic collapse and the Allied invasion of the formed Soviet Union. Lenin thus had to be quite practical, and first order priorities were holding the country together and stabilizing the political situation to prevent further invasions by the hostile western countries and secondly to industrialize the economy in order to have resources to transform the mode of production. He openly admitted that capitalism would be preferrable to the current state of Russia. Lenin actually openly and often denied that Russia was socialist, but rather that it was their goal:
No one, I think, in studying the question of the economic system of Russia, had denied its transitional character. Nor, I think, has any Communist denied that the term Socialist Soviet Republic implies the determination of Soviet power to achieve the transition to socialism, and not that the new economic system is recognized as a socialist order
In fact USSR was first announced to have "reached socialism" under Stalin, who had - yes - greatly industrialized the Soviet Union, but not fundamentally changed the mode of production to a socialist one. Since Stalin was, before replacing Lenin a serious scholar who had analyzed much of Lenin's and Marx's writings well aware of socialist theory, it can be quite confidently be said that this announcement was made in order to advance Stalin's personal cult inside the Bolshevik party and as a propaganda message to promote Stalin's Russia. So now, officially, USSR was in fact a socialist state whose goal by the ML-definitions of the words, was communism.
I am from a former soviet country, and it is important that these ideas were somewhat new and there are some inconsistencies in the terminologies until later when they were defined more properly. Many took the word social and commune and tried to make a government definition run by social/communes. - Even Karl Marks used the words interchangeably.
So the trend from Capitalism to the paradise of Communism is supposed to happen in stages.
seize the means of production (land, labour, capital , and resources)
Establish a union state controlled by the workers.
redistribute resources each according to his need/ contribution depending on stage.
Once capitalism has been abolished and wealth has been redistributed , then dissolve into a stateless, classless, money-less, society.
The last part being important. The USSR , nor any other socialist state has ever dissolved into anything except for capitalism.
They called themselves socialist because they were in that stage of development . There is a communist party which was supposed to keep the progress moving forward to achieve the communist dream. However, Communism wasn't achieved and therefore the USSR isn't communist , but Socialist.
The Communist Party of the Soviet Union (Bolshevik) nominally advocated for an eventual classless society. Much like the reformist Fabian socialists did.
Attempts by Soviet proletarians to advance their own interests at Kronstadt or the Ural-Siberian method were not effective. The SDLP(b) or CPSU(b) foiled and fouled such efforts.
Efforts towards generalised proletarian self governance in 56 (Poland and Hungary) or 68 (Czechia of Czechoslovakia) were militarily defeated by Polish or Soviet parties.
The analysis is either: communism is bullshit. Or, that making ideological claims about what you wish is utter bullshit when you shoot proletarians to defend an ideology not built out of factory praxis. That is to say that you can put lipstick on a pig, but when you put a sausage in its mouth it will be bitten off.