To me, USSR seems like a very conservative name for a nation that, from what I know of history, basically wanted to be the antithesis of Western Capitalism.
Yet they decide to name their country in a similar manner as the U.S., who would ultimately be their greatest rival.
Is there a reason that they decided to use "socialist" rather than "communist" or "Marxist"? Why call it a Republic if that's not really what they had? Etc.
I don't really know where to begin.
What do you take 'socialist' to mean?
In Marxist theory, it simply doesn't make sense to talk about a 'Marxist Republic' or a 'Communist Republic'. Marxism is a political philosophy, economic analysis and method for political action. Communism is a level of human social development marked by a stateless, classless society.
On paper the USSR was an international union of 15 states, but in practice dominated by Russia and the bureaucracy based mostly in Moscow. 'Soviet Socialist Republic' tries to describe the state form of the system of government that arose in the former Russian Empire where the working class had seized power in October of 1917.
Capitalist countries often describe themselves as 'liberal democracies', with state forms like Parliamentary Republic, Presidential Republic, Constitutional Monarchy etc; these are countries where the capitalist class is the ruling class. Marxists would therefore call them "bourgeois democracies" (bourgeois = capitalist). A socialist system where the proletariat (working class) is the ruling class would therefore be called a 'proletarian democracy'.
The Soviet system arose in the Russian Empire during the struggle against Tsarist autocracy and capitalism. They were broad committees of working people, based in towns, villages, city districts and workplaces. When the Tsar was overthrown in February 1917, the Soviet in Saint Petersburg acted like a second legislative house to the Duma (a bit like how the USA has the Senate and House of Representatives, but imagine that each house wanted the other abolished!). This system of Dual Power collapsed when the Provisional Government betrayed their promises to the revolutionary masses and could not defend itself against an attempted reactionary coup d'état by General Kornilov. The bourgeois Duma and Provisional Government were overthrown by the revolutionary masses and Lenin famously declared "All Power to the Soviets!".
From then on, the system of Soviets fought against counter-revolutionaries to become the structural basis of the State: a new, workers' state, rather than the Tsarist autocracy or bourgeois dictatorship of the rich. Soviet Socialist Republics (SSRs) were formed in Russia and all the oppressed countries of the Russian Empire, like Ukraine, Kazakhstan etc. These SSR's were united together by the foundation of the Union of Soviet Socialist Republics in 1922.