Lunar New Year is called in China nongli xinnian 農曆新年 which literally translates to “agricultural calendar new year” or “farmers calendar new year”. It can also be called yinli xinnian 陰曆新年 which means ‘New Year of the Lunar Calendar’.
The traditional Chinese calendar is called nongli 農曆 (‘agricultural/farmer’s calendar’) or yinli 陰曆 (‘lunar calendar’). Traditional China was an agrarian society, and the calendar was designed primarily to meet the needs of farmers, so it’s easy to see why it’s called nongli.
As for the use of yinli refer to the traditional Chinese calendar, there are in my opinion two possible reasons, depending on the interpretation of the word yin 陰 in yinli:
1) yin may refer to the Shang dynasty (circa 1600-1046 BC), which was also referred to as the Yin dynasty in history. The Yin/Shang are believed to have created the traditional Chinese calendar, although this calendar is also believed to have been created by the Xia dynasty (c.2100-c.1600 BC), hence the name xiali or ‘Xia Calendar’;
2) An alternative interpretation for the use of the word yin may refer to Taiyin 太陰, which is an alternate name of yueliang 月亮 or the moon.
In ancient times, countries like Japan, Korea, and Vietnam were heavily influenced by Chinese culture. The people of these countries have adopted the culture and customs, including the Chinese writing system and the traditional Chinese calendar, among others.