If you want to compare the organization code (int) with the name (String) it would be something as simple as:
int codigo_empresa = 5;
String nombre_empresa = "5";
int comparacion = codigo_empresa == Integer.parseInt(nombre_empresa)? 0 : codigo_empresa < Integer.parseInt(nombre_empresa)? -1 : 1;
Being that if the comparison is 0 are equal, if it is -1 the code is smaller and if it is 1 is greater.
But I sincerely doubt that this is what you want, if you want to order by your code and then within that order by name something like
cod nombre
01 a
01 b
02 a
02 c
Well in that case first order them by code and separate them into different lists and then alphabetize them, to sort alphabetically you use the function.
Collections.sort(nombre_array_strings);
I hope it helps you.