This guy doesn't get a name, but he doesn't really need one because he's here to serve as the novel's Big Bad. When Sasha first sees him, he's there to arrest his dad. Strike one. He's got "bloodshot eyes" and smacks Sasha's dad around (5.16), before hauling him off to prison. Strike two. And finally, at the end of the novel, he seals Sasha's dad's fate and gives the kid a cruel ultimatum: Sasha can either be a spy for him, or he can go to prison. Strike three, wouldn't you say?
It might help you to think of this ominous dude as a human stand-in for the Soviet State. Since Joseph Stalin is not really a character in the book (other than in Sasha's day dreams), this guy gives us a decent picture of how power was exercised in Soviet society (and the picture definitely isn't pretty). His cruelty represents the entire oppressive system that Sasha must face, and his actions and words give us a more immediate feel for how things work, compared to the more remote and idealized figure of Stalin.
Just as everyone in the komunalka is afraid of Sasha's dad, everyone is also way scared of the Senior Lieutenant whenever he pops on the scene. He has a super commanding presence about him, as when he appears in the school in chapter 20. He doesn't yell or throw around threats, but rather just expects that when he talks, people will listen. Oh, and confess to their crimes right quick.
It's the Senior Lieutenant who finally dashes any of Sasha's hopes about his dad returning. He also throws in a few hard truths for the boy: he tells him that his mom didn't die in a hospital after all, and that his dad actually turned her in as an enemy of the state (28.15). As the bearer of this bad news, the Senior Lieutenant will always be associated with brutal oppression of the Soviet system that Sasha has now come to understand.