No.

If string_name is declared:

    int string_name;

you would use foo(&string_name, 1) so foo()'s str parameter points to string_name.

If string_name is declared:

    int string_name[n];

you would use foo(string_name, 1) so foo()'s str parameter points to string_name[0].

FWIW, convention suggests that a "string" is a NUL-terminated character string (i.e., an array of characters), not an array of integers.