To keep things simple, we can use names that were used on maps of that time and that field marshals of one side or the other would read when planning missions. For the German side it would be German maps with Russian names in Latin alphabet - but even that is complicated and there is no right version, the best thing we can do is find a name they used back then and put it on map.
What is now Latvia and Estonia were Crusader/church states in 13th-16th century so the large cities and medium towns had German names and Saulai in Lithuania was Schaulen although as far as I know the Crusaders never ruled there, but the city was close to their lands and they gave it a German name. I have used as much of these names in Riga and Tallinn/Reval scenarios as I could find.
On the Soviet side, we have Russian names but in Latin alphabet and the game is in English and German versions, so the Soviet capital is either Moskau if you try to take it or Moscow if you defend it, although Russians call it Moskva... this is as simple as it gets, and still very complicated.
(By the way, Major von Boehm and his colleagues in the movie about interrogation speak English most of the time and their files are in English, so that the American pilots of 1944 could understand everything without spending some months on a beginner course in German.)
Anyway, if you need help with Russian names let me know.