(And it is Koróv'ev, not Korovyóv, as the otherwise wonderful Burgin-O'Connor translation has it)
Koroviev's name, like Woland's nationality, is merely tentative: "My name? let's say Koroviev." Koroviev is derived from korova, "cow," and may be compared to the name of a character in A. K. Tolstoy's Upyr' [Vampire], the vampire Telyaev [Calf]. Telyaev is also the knight Amvrosii. Bulgakov uses the name Amvrosii in Chapter 5 for one of the regulars at Griboyedov, and in Chapter 32 Koroviev turns into a dark-violet knight just as Telyaev turns into the knight Amvrosii in Tolstoy.
One of Woland's band, Korovyev usually wears a checked jacket, jockey cap, and pince-nez, which costume recalls that of the devil who appears to Ivan Karamazov in Dostoevsky's Brothers Karamazov.
Koroviev's profession as (ex-) choirmaster connects him with E. T. A. Hoffman's character, Kapellmeister Kreisler.
Fagot--Korovyev's second name means "bassoon," which connects him to the musical themes of the novel (remember that he's also a retired choirmaster).