I see no problem with the use of  "Chinese New Year" 

Because the lunar calendar was invented by the Chinese in their ancient time, according to Shi Ji(the most reliable history record of Chinese history before the Han Dynasty), and can be traced back to the time of Huang Di(The Yellow Emperor) who lived in the era around 2500-3000 BC. That is a history of about 5,000 years or more. So the Chinese have no doubt own the credit. Do not let politics, jealous or racism blind your wisdom ,guys.