What fish should be chosen for the New Year dinner is based on auspicious homophonics. Steamed fish is one of the most famous Chinese New Year recipes. This is practiced north of the Yangtze River, but in other areas the head and tail of the fish shouldn't be eaten until the beginning of the year, which expresses the hope that the year will start and finish with surplus.
The fish should be the last dish left with some left over, as this has auspicious homophonics for there being surpluses every year. Chinese people always like to have a surplus at the end of the year, because they think if they have managed to save something at the end of the year, then they can make more in the next year.
Fish is a traditional Chinese New Year dish on the Chinese New Year dinner menu. In Chinese, 'fish' (鱼 Yú /yoo/) sounds like 'surplus'.