The Russian Federation is called the Russian Federation because it is a federal republic, but that's a bit of a circular answer so I will provide some further background. I'll try to do a very brief rundown of Russian constitutional structure and nationality policy (they're related) from 1917 to now.

First I'll note that there actually never was a "Russian Soviet Socialist Republic". The entity that the Russian Federation is actually descended from is a mouthful that was known as the Russian Soviet Federative Socialist Republic (hereafter RSFSR because even I get the name mixed up).

The Russian Empire had been for the most part a unitary state - despite it having provinces, everything was directly controlled by the central government (and that government largely controlled by the tsar). The February 1917 revolution had replaced this government with a republic under the control of a Provisional Government and the Petrograd Soviet - there was no clear constitutional structure for the country, and elections to a Constituent Assembly were scheduled for December 1917, with the assembly to write a new constitution and sort everything out. The Petrograd Soviet (and soviets in general) by the way was not originally something controlled by the Bolsheviks, but a workers' council.

Anyway, before the Constituent Assembly elections, the Bolsheviks managed to gain a majority in the Petrograd Soviet and also overthrow the Provisional Government. They only got about 25% of the vote in the constituent assembly elections, and so closed that body down after one day of meeting. They then went on to write their own constitution that was adopted in July 1918 for what was officially now known as the RSFSR.

The RSFSR reflected a lot of Lenin's ideas around the nationality question, namely that non-Russian ethnicities should not be oppressed by "Great Russian chauvinism", but should have as much autonomy as possible (as long as that autonomy broadly stayed within the confines of socialism acceptable to the Bolsheviks). A big part of this was for tactical reasons, as numerous nationalities of the former Russian Empire had already declared independence, or had asserted a great deal of local control.

As such, the 1918 constitution asserted:

"The Russian Soviet Republic is organized on the basis of a free union of free nations, as a federation of soviet national republics."

And also explicitly recognized the independence of Finland and the right of Armenia to "self-determination".

The federation was supposed to be voluntary:

"In its effort to create a league- free and voluntary, and for that reason all the more complete and secure- of the working classes of all the peoples of Russia, the Third Congress of Soviets merely establishes the fundamental principles of the Federation of Russian Soviet Republics, leaving to the workers and peasants of every people to decide the following question at their plenary sessions of their soviets, namely, whether or not they desire to participate, and on what basis, in the Federal government and other Federal soviet institutions."

Anyway - as matters turned out, there were parts of the former Russian Empire that were not part of the RSFSR, namely Byelorussia, Ukraine, and the Caucasian countries of Georgia, Armenia and Azerbaijan. Through the Russian Civil War these republics ended up under Bolshevik control by 1921, but were still formally independent countries, whose ruling parties happened to be sections of the Bolshevik Party in Russia, and whose foreign relations operated out of Russian embassies. There was some internal debate over how to reorganize matters. Stalin favored absorbing these republics directly into the RSFSR, but Lenin opposed this, and his view prevailed. This resulted in the 1922 Union Treaty which established the USSR.

The USSR then was actually a federation of federations: the member states were the RSFSR (a federation), the Transcaucasian SSR (which was a federation of Georgia, Armenia and Azerbaijan), and the Byelorussian SSR and Ukrainian SSR, which weren't federations. A constitution for this union was enacted in 1924, with newer ones in 1936 and 1977. The RSFSR itself got a new constitution in 1937 and again in 1978 to mirror the changes to the Soviet constitution. Of particular note in the 1977 Soviet constitution is the right of member states to secede from the Union, which was pretty much an unlikely and empty right as long as the Communist Party of the Soviet Union maintained its constitutionally-guaranteed monopoly on power across the USSR.