Not sure if I'm allowed to comment here but I'll give it a try. Short answer; the 20th century was an incredibly volatile time in Russian history. There were several major regime changes and each regime renamed some of the cities in order to symbolize that they were breaking from the past and "restarting" for lack of better word. I'm addressing each example below.

St. Petersburg

St. Petersburg was founded by Peter the Great in the 1700s. Peter the Great was trying to break with the previous Tsars (Russian rulers) and one of the ways he did so was by building a brand new capital city in order to get away from the established political families of Moscow. Peter the Great's lifelong goal was to transform Russia into a Western European style empire. As a result, St. Petersburg was given a German name and the city has Baroque inspired architecture and canals modeled after Amsterdam. In Russian, Saint Petersburg would be Sankt Petrograd.

This lasted until the outbreak of WWI. The Russian Empire was fighting against Germany and the Central Powers. St. Petersburg is a German name, so during the war the city was renamed the Russian version, Petrograd, in 1914.

Long story short, WWI was a disaster for the Russian Empire and it was one of the causes of the Russian Revolution. After the Revolution, the Bolsheviks (Communist Party) took control of the Russian Empire and formed the USSR. In order to symbolize their victory, Petrograd was renamed to Leningrad, after Vladimir Lenin, the head of the Bolsheviks, in 1924.

Flash forward to 1991. The USSR collapsed for many different reasons and the citizens of Leningrad voted to change the name back to St. Petersburg now that the Communist government is no more.

Tsarytsin-Stalingrad-Volgograd

Tsarytsin is named after the Tsar, and the Bolsheviks overthrew the Romanov Tsars, eventually forming the USSR. The Soviet government, not sure exactly when, renamed Tsarytsin to Stalingrad after Joseph Stalin. Stalin is the Communist leader who came to power after Lenin's death. Stalingrad is also where the very brutal Battle of Stalingrad took place during WWII.

Then in the 1960s following Stalin's death, the next Soviet leader, Khrushchev, instituted a bunch of reforms in order to for lack of better word "repair" the USSR from the damage Stalin did during his reign. Stalin was a totalitarian dictator and his actions and policies resulted in: mass starvation during the Holodomor, massive deaths during WWII, massive deaths of dissidents, political prisoners, various ethnic groups, Jewish doctors, people who laughed at anti-Soviet jokes, and innocent people in the wrong place at the wrong time during his Purges. So Khrushchev, wanting to "de-Stalinize" the USSR had Stalingrad renamed to Volograd after the river Volga which flows through the city.

Yekaterinburg

Like Tsarytsin, Yekaterinburg is named after a pre- Soviet Russian royal. In this case, Peter the Greats wife, Catherine (Yekaterina is the Russian version of Catherine). So as with the other cities, the Bolsheviks, wanting to erase all mention of the Tsars and Russian Emperors, renamed the city after Sverdlov, another Bolshevik leader.

Then flash forward to 1991 and the fall of the USSR, and Sverdlovsk is renamed back to Yekaterinburg. Although the oblast (province) that Yekaterinburg is in is still named after Sverdlov. I am not sure if the city's name was changed by referendum, post-Soviet leader Boris Yeltsin, or by local politicians.

I hope this helps and if anyone wants me to expand on something or to see any sources, please let me know.

I want to add some notes to the answers by /u/hemblurneene and /u/kaisermatias.

The first name change in the Soviet regime that I know of was the change of Ekaterinodar (Catherine's gift), the capital of Kuban in South Russia, to Krasnodar (Beautiful/Red gift) in 1920. The capture of one of the Cossack's main city from the Whites, and the place where the first White leader Lavr Kornilov was killed in 1918 by Red artillery (a guy who almost became dictator of Russia in August 1917), was a huge propaganda victory for the Red Army. Thus, the soviet leadership decided to change its name from the monarchical "Catherine's gift" to the more poetic "Red gift".

The first name change in the Soviet Union after a person was Leningrad, and it was done in 1924, after Lenin died. The Communist Party decided to change the name of the city that gave birth to the revolution to their recently deceased leader, as part of a country-wide glorification of the cult of Lenin, which included embalming his body and put it in a mausoleum in Red Square. His native city of Simbirsk was also renamed Ulianovsk in his name.

This led to also changing Russia's third largest city and gate to Siberia, from the Imperial Yekaterinburg to Sverdlovsk, named after the first Secretary of the Communist Party during the Revolution and Civil War, and founding member of the Politburo Yakov Sverdlov, who had died in 1919.

After these changes, they just kept coming. Tsaritsyn was renamed Stalingrad in 1925 after the proposition of some over-zealous ass-lickers of the dictator, whose power was just being consolidated, to which most of the Party agreed. Stalin had been the Bolshevik leader in Tsaritsyn during the Civil War, and presided over the bloody Battle of Tsaritsyn against the Whites. In the Volga city Stalin first tasted dictatorial powers, over-zealous repression, and distrust of so-called "former peoples" or "class enemies" in the shape of former tsarist officers in the Red Army. While he was in Tsaritsyn the rivalry between him and Trotsky, Commissar of War, was formed.

The renaming were usually a show of propaganda or a way of honouring the dead bolsheviks. Nizhny Novgorod was renamed after its son Gorky, after the influential proletarian writer came back from Italy in 1932. Vyatka was renamed Kirov after his assassination in 1934. Samara was renamed Kuybyshev after his death in 1934. Königsberg was renamed Kaliningrad after the death of Kalinin in 1946. And together with the big cities, many small towns and random associations followed.

/u/hemblurneene covered most of what I wanted to say, so I'll just quickly touch on a few things:

A lot of the names that were initially changed by the Bolsheviks had tsarist associations, so that couldn't last. Many cities and towns adopted names from leading Bolsheviks (Leningrad, Stalingrad, Sverdlovsk, and so on), while Stalin in particular had many named for himself during his time in power. Once he died the process of destalinization took place throughout the 1960s, and a lot of places named after Stalin reverted back to their original names. This repeated itself again in 1991 when the USSR collapsed, and several cities went to pre-Soviet names.

However some did not: as noted above the oblast (region/province) that Yekaterinburg is located in is still named Sverdlovsk, and the same is true for Saint Petersburg: the oblast around the city retained the name Leningrad, which is in part because in 1991 there was a city-wide referendum on the name, and it was voted to restore it to Saint Petersburg. The oblast was not part of the vote, so never changed, and there hasn't been any pressure to do so since then.

And I will add a couple sources, just because it is an interesting topic (and the journal article is one of my more favourite ones, for the sake of existing):

• G.R.F. Bursa, "Political Changes of Names of Soviet Towns" The Slavonic and East European Review Vol. 63, No. 2 (April, 1985): pp. 161-193. This is more about the initial wave of Bolshevik changes, and the destalinisation campaign of the 1960s.

• John Murray (2000), Politics and Place-Names: Changing Names in the Late Soviet Period, Birmingham: Department of Russian, University of Birmingham. This is one I haven't actually read (though have cited based on partial readings), but it gets into the post-Soviet changes, and thus serves as a nice compliment to the Bursa article.

You may be also interested in a more general response to a similar question I wrote in this thread.