The Party took the name Communist Party of the Soviet Union in 1952 . In other republics , communists established the Armenian Communist Party , Communist Party of Azerbaijan , Party of Communists of Kyrgyzstan , Communist Party of Ukraine , Party of Communists of Belarus , Party of Communists of the Republic of Moldova , Communist Party of Kazakhstan and the Communist Party of Tajikistan . Along with the CPRF , these parties formed the Union of Communist Parties - Communist Party of the Soviet Union .