This is a link to a story about a missile launch from a Russian submarine, “Emperor Alexander III”.
Why would they name a sub after the father of the Tsar they murdered in the revolution?
I don’t think Russia is part of the Soviet Union nowadays, so it’s not clear who you mean by “they”.
Not surprising that the current regime would decide to honor a ruler who believed in unlimited autocracy and hated Jews.
Perhaps so. I would think they would want to preserve some connection to the USSR.
Who are “they”? 
The current Russian government.
So the current Russian government named the submarine, and the current Russian government murdered the czar?
I think your OP has too much ‘they’.
Putin has never been an ideologue. He considers his regime to be the legitimate successor to all previous regimes, Tsarist or Communist. He wants people to be loyal to him, and he will appeal to Soviet nostalgia, or Tsarist nostalgia, or whatever he thinks will work.
The latest generation of ballistic missile submarines all seem to be named after monarchs. The destroyers are named after Soviet-era generals and admirals. Putin considers all of Russian history to be his.
Why? While there is a mild resurgence of nostalgia for the Soviet era, where goods were scarce and corruption was rampant but at least someone was in charge and Russia was viewed as a legitimate superpower, there is also a cultural memory of the wide ranging purges during the Stalin regime where people were arbitrarily arrested and convicted in show trials, and the generally poverty which was rampant throughout the existence of the CCCP which had several generations of a family living in a single flat with communal kitchen and toilet facilities. All of the cities that were renamed during the Soviet era such as Leningrad have been returned to their pre-Soviet names, and most of the Soviet-era iconography has been removed (and often sold to Western collectors for kitsch value).
While the Marxist-Leninist takeover of the Russian Empire was essentially just another autocratic regime with socialist trappings, swapping out the mostly inherited Tsarist absolutism for a reign of self-appointed oligarchs under the branding of Communism, it never carried the same sense of international prestige as monarchy (no matter how incompetent, unstable, and destructive the tsarist regimes were) and in many quarters there is still an cultural undertone of resentment for the execution of the Romanovs. The resurgent popular myth of Russia as the center of “World-Island”, and especially as “The Third Rome” (the ostensibly legitimate successor to the Roman Empire) is innately tied to the Tsarist regime starting with Ivan III Vasilyevich and his marriage to Sophia Palaiologina.
As @mbh noted, Putin isn’t any kind of ideologue, and certainly not of Marxist persuasion. He’s essentially a masterful troll who manipulated his way into control of modern post-Soviet Russia by equal measures of political skill, a willingness to undercut anyone who might challenge him, and no small degree of good fortune. To that end, he’ll make claims that contradict each other in the same sentence and appeal to any nostalgia that will garner public enthusiasm. Julia Ioffe’s limited podcast series “About A Boy: The Story of Vladimir Putin” doesn’t really go into all of the gory details of his ascendence but focuses on what made him the creature he is, and dissects his autobiographical claims in the context his upbringing in post-WWII. It’s far from the last word on Putin (and relies on a lot of third-party sources and general cultural information from her father, who grew up in similar conditions in Russia) but it provides a lot of useful insight on why Putin says and acts the way he does that a lot of political and military pundits miss.
Naming submarines after Tsars is exactly in line with the appeal to the cultural view of Russia as a former Great Power held down by the boot of the NATO alliance, never mind how ineffectual NATO has become, evidence of how hollow the military and economic might of the Russian Federation is, or the oncoming massive demographic collapse of Russia and Eastern Europe in general even before most of its brightest and most capable young adults started fleeing like rats from a sinking ship.
Stranger
I can’t believe Americans are putting Harriet Tubman on their money when their founding fathers used to keep Black people as slaves.
Not all of them did and many were abolitionists. Are you saying we should never honor African Americans? What is your point?
Turing was put on UK notes
I think the point was,“regimes and people change and so there is no mystery about Putin naming a submarine after Alexander III.”
Oh! They were saying it’s the same thing. Just like I was. lol
The long and short of it: it’s a RUSSIAN vessel, not a Soviet vessel.
And the current government did more or less apologize for shooting the Romanovs.
I just thought the Tsars would be bad guys in Russia, no matter who ran the government.
Alexander III was a tough guy. Held up the roof of a crashed railway car while his family escaped, and tied some Austrian(?) guy’s fork into a knot at a diplomatic discussion.
If we have come full circle, then I guess it must be time for another proletarian revolution.
Russians prefer a strong leader over a ‘fair’ one, and as bad as the tsars treated the Russian (and other) people, the komissars were even worse.
Stranger