In WWII, there were two major 'sides' fighting against each other, the so called Axis Power (which main members were the Nazi Germany, Italy and the Japan Empire) and the Allied Powers (which main member were the USA, the UK, the Soviet Union and China).
If the question refers to one of these parties, I don't believe any one of them was called 'communist'. The Axis Power was mostly formed by extreme nationalists/fascists governments. And the Allied by republics (USA, China), the monarchic UK and the Soviet Union was the only one ruled by its respective communist party, the CPSU (who ruled from 1925 to 1952), born from the Bolsheviks wing of the RSDWP (Russian Social Democratic Worker's Party).
I hope this helps!
