Is it the same for different provinces to modify the surname of China people?

As far as I know, no, a child's surname can only be given to his biological father or mother, not to a third person. Nowadays, many family surnames, especially those in rural areas, will be changed back to their original surnames according to three generations, so that children will not take their father's surname or their mother's surname. This is illegal, and there will be problems in handling children's accounts.