New Year 新年(Xīnnián) in China can be meant two different moments: January 1st or Spring Festival.  Even though we are using Gregorian Calendar offically, most Chinese still consider Spring Festival the "real" New Year.  In January you can often hear people say "next year" which actually means a month or two, not 356 days later.

January is usually called 一月 (Yīyuè), numerically accented like other months.  It is also can be seen as 元月 (Yuányuè) in your calendar.   January 5th can be called 元月五号 (Yuányuè wǔ hào), for example.  In addition, January 1st, 一月一日 (yīyuè yī rì) is an official festival 元旦 (Yuándàn) or 元旦节 (Yuándànjié), everybody has one day off.

So what about Chinese New Year?  How do you call it?

The real 新年(Xīnnián) and the biggest day of the year for most of Chinese officially is called 春节 (Chūnjié, Spring Festival), for it is always close to 立春 (Lìchūn), the first of the 24 Solar Terms in Chinese Calendar, which signifies the beginning of spring (春天 chūntiān).  The first month of Chinese New Year is 正月 (Zhēngyuè), note here 正 is pronounced in first tone.  

To distinguish these two New Years, some people greet 新年好! (Xīnnián hǎo!) in January and 春节好! (Chūnjié hǎo!) or 新春快乐! (Xīn chūn kuàilè!) in Spring Festival.