My daughter was born on the sixth day of August. Her surname is Chen. Give me a name with wood, preferably three words. Thank you.

The five elements lack wood. I think these words are better: Lin, Shan, Mei, Feng, Jie, Liu, Bai, Rou, Hua, Sang, Bin, Sen, Chu, Lin, Shen and Zi.

If you don't want a single name, these names are good:

the Chen Dynasty