You didn't provide the answers, however, European Communist countries didn't have much choice since they were liberated by Communists during the war. The Asian countries did have a choice and chose to adopt it which is why there were many wars, both civil and one country fighting another like in Vietnam or Korea. They were supported by the Soviets and China.
Is this your answer and if so you are welcome
Answer:
According to Klaus Klostermaier, the term Vaidika dharma is the earliest self-designation of Hinduism. According to Arvind Sharma, the historical evidence suggests that "the Hindus were referring to their religion by the term vaidika dharma or a variant thereof" by the 4th-century CE