Founded in 1964, the only Soviet approved record label was Melodiya. It was a state enterprise that predominantly sold 33s and 78rpm records.

Mostly Melodiya produced classical music from Russian cultural giants: Tchaikovsky, the conductor Alexeev, Borodin String Quartet. You could purchase recordings of Soviet plays and fairly tales. By the 1970s there were Soviet “rock” groups but most of the catalogue was still classical Russian music, ethnic folk music from Soviet states, and radio plays.

Notably absent in the period you are looking for was foreign music. As part of the broader cultural strategy of homegrown pride, international artists were not printed by Melodiya initially. By the mid-70s you could get some ABBA or other European records but these were scattershot and hard to come by.

Source: The Great Soviet Encylopedia, version 3 (1974)

The company actually still exists today: https://melody.su/en/