How about the father’s surname is Chen and the mother’s surname is Yang, and the girl’s nickname is Yang Tao?

No, since it’s a girl, let’s call her “Chen Liu Miao”. She has both her father’s and mother’s surnames, and the mother’s surname is invisible. Whenever I see the word “Yang” alone, I think of “Yang Liu”. The word "Liu" is also in line with Chinese people's naming habits. Is "Miao" a derivative? I feel it is very good and smooth, and I hope to adopt it.