Answer:
There are no actual names given for "noncommunist"
Explanation:
First of all, your question is vague as the name "Russia" can be interpreted in different ways. Whether it is Post-Cold War Russia, Soviet Union, or Pre-Soviet Russia. I assume that you want an answer for the Soviet Union so I'll answer that.
The closest name or nickname given to people who were noncommunist or anticommunist was "Whites". Throughout the Russian Civil War between the Bolshevik Red Army and the White Army, many of the Bolshevik soldiers and government officials called the people who participated in the opposing coalition as the Whites. Otherwise there are no clear names given for noncommunist or anticommunist individuals.
In a likelihood, most individuals who did not follow communism or was against communism in the Soviet Union/Russia were punished, imprisoned, exiled or executed. They're simply regarded as a spy or enemy of state.
