I dont know the exact origin of that nickname, But Chinese figure skating community call them "Cong Ge" and "Tong Mei" separately. "Ge" means older brother and "Mei" means younger sister. "Cong" obviously is originated from Han's given name, I am not sure how Sui, got the nickname "Tong". Perhaps something related to her flexibility or body type when she was still a junior.that she did not have womanly waist line yet, so that kinda children's "H" body type, resemble a barrel. which has the pronunciation "Tong". And Han hold/lift Sui like holding/liftig a barrel.

But I am not sure. in all means, that's their loving nicknames among Chinese figure skating community, and Both of them are cute as a button