In Spanish the definite article must be used if the person is not named. So you should say: "El perro del nino no es blanco"
In other sentences if person name is given you could say: "El perro de Juan no es blanco"
You have to indicate the possesion.Use DE for 'S. First the possession LA CAMISA, then the union DE, and at last the owner EL HOMBRE. Note: when do you use de + el, combine it DEL. So, La camisa del hombre.