First of all, I have to say that renaming of cities, streets and so on is not as trending as it seems. It is quite expensive and often controversial.

Yes, Leningrad is now Saint-Petersbourg, and Kalinin is now Tver, and other Kaliningrad (yes, there were two Kaliningrads in the USSR) is now Korolyev, but there is still Ulyanovsk (ex-Simbirsk; it is named after Vladimir Lenin, since his real surname was Ulyanov), Dzerzhinsk (it is named after Felix Dzerzhinsky, the first Cheka/OGPU boss), Engels (it is named after Friedrich Engels) et cetera.

Almost in every russian city one could still find Lenin street (улица Ленина), because no-one cared to rename them. There is Leninsky prospect (Lenin's avenue) in Moscow. Also in Moscow one of the subway station is named after the guy who was the main executioner of the last emperor, Nicholas II. It's Voykovskaya (Войковская), and his surname was Voykov.

And Nicholas II is an orthodox saint.

So, sometimes it seems irrational. They renamed Gorky street (улица Горького, after Maxim Gorky, writer) to Tverskaya street, but Gorky Park is still here. Voykovskaya is still here. Or, there is Yekaterinburg (soviet name: Sverdlovsk) but it is the center of Sverdlovsk region (Sverdlov is quite famous bolshevik, and the region was not renamed).

The thing is, these renamings were driven not by hate to bolsheviks but mostly by desire to go back to russian historical roots. So, Tverskaya was renamed not because Maxim Gorky was a bad guy (he was just a writer after all), but because Tverskaya is the historical name of this street. Dzerzhinsk that I mentioned earlier is a new city, it doesn't have an old name, so it is hard to rename it. There were some proposals to rename Ulyanovsk (to Simbirsk) but it seems that people from this city used to Ulyanovsk, and they're against renaming.

So, what do we have with Kaliningrad. Kaliningrad was Königsberg, it was a german city, and it doesn't have an old russian name. There were some proposals to rename it (this one, for example), but it's highly controversial because the real historical name for Kaliningrad is Königsberg, there is no russian option, and, I quote, "it could be seen as a symbolic step to start new discussions about WWII results".

So, the answer to your question — there is no other name for Kaliningrad, and Königsberg is too controversial. Also, all these renamings were not so politically charged as you may think, the main idea behind them was to restore 'real' historical names.

Regarding Kalinin, it's quite complicated. I don't think I'm qualified to fully answer this question, and I'm not sure if this is a historical question, so I'll give a very short answer. If we're talking about modern Russia, bolsheviks are not the main bad guys at all. They're just part of a history. Some of them are very controversial or generally bad guys (Beriya is a universal bad guy, and Stalin is extremely controversial), some of them perceived as not so bad (Lenin is still controversial, but he is viewed as much more good guy than Stalin), and Kalinin is not controversial at all. For the majority of russian people it's just a name, they don't know and don't care whether he was good or bad.