So, we have names for the various Soviet sub classes like Typhoon and Akula. And I vaguely remember that they call their sub classes something else.
What did they call our sub classes? 
I think the question is “What do the Soviets call the US submarine classes, or do they just use the names we use?”
I know what we call them, mrAru was a submariner for 20 years. What we call an Akula class submarine was called variously **Щука-Б/**Shchuka or Bars class. [how does one capitalize a shch when it is one letter in cyrillic?]. Did they randomly call the USS Spadefish “осетр” because it was a sturgeon class sub, did they know it as something else? How about the USS Miami, we stopped giving them class names, the ‘class sub’ was the USS San Juan … they were 688i [improved] class subs. Did they call them whatever 688 was in Russian?
We didn’t stop giving submarines class names. The USS Miami and USS San Juan are both improved Los Angeles-class attack submarines.
The USS San Juan and subsequent boats, while getting some major modifications (including the AN/BSY-1 combat control system, hardened sail, and bow planes) are still considered a type of Los Angeles-class submarine. Among other things, they still have the same basic hull shape and layout.
P.S. I’m not sure what the answer to your original question is, but would be curious to find out.
I’m sorry, aruvqan, I misunderstood the question. My apologies.
NATO reporting names were partly since the actual Sov designation was usually not known when intel discovered the existence of the system. Why would the Sovs need to use reporting names different from the class names, since the US class names were actually known?
BTW, the did the Russian’s not call the Typhoon; Akula?
They called one the Akula, the others had their own names - sort of like mrAru was on both the Miami and the San Juan.
Useless skill - I know how to turn off the commander’s hot water recirc pump on the Spadefish, may she rest in pieces. 
Also creepy fact - she had a number of parts that were originally designated as replacement parts for the Thresher :eek: which would probably make for a great plot in a sub based horror movie.
And one of the saddest pictures I have run across online was the one of multiple subs that were part of the Northern Fleet sitting at the pier rusting. What a waste of huge amounts of money, the crews apparently moored them and walked off [well, the money stopped.] Though what they could have done to keep the fleet together I don’t know, USSR blew up - at least we have not blown ourself up yet so we could use some subs for research purposes in a pinch.
If a certain “authoritative” source (a guy named Clancy, wrote a few submarine-based books, rest his soul) was to be believed, the US/NATO names for Soviet submarines was because the Soviets never publicly released the names of individual ships or classes. Thus, NATO gave the letter-based names (alfa, foxtrot, golf, etc), plus the Typhoon and Akula) in-house just to have something to call each ship. I’m sure the various navies knew the real names, but that would have given away an espionage secret to the other side.
I always figured someone in the USSR just picked up a copy of the most recent edition of Janes Fighting Ships or the May issue of USNI Proceedings for the Naval Review and knew the names, dates of birth, and every other conceivable bit of information about the newest everything in the US fleet.
From all I’ve read, the Soviets referred to our subs by the same English-language names we used.
Makes sense. I actually ran into Tom Clancy on base here when he was doing some sort of research back in the early 90s.
Thanks=)