DECLARE
  l_err_code VARCHAR2(512);
BEGIN
  FOR cur_r IN (SELECT id, surname FROM some_table)
  LOOP
    BEGIN          --> note this inner begin-end block! It will make possible
                   --  to continue the loop even though an error appears
      INSERT INTO another_table (id, surname)
        VALUES (cur_r.id, cur_r.surname);
    EXCEPTION
      WHEN OTHERS THEN
        l_err_code := sqlerrm;
        INSERT INTO error_log_table (id, err) VALUES (cur_r.id, l_err_code);
    END;
  END LOOP;
END;

SQL> CREATE TABLE name_table(id NUMBER PRIMARY KEY, surname VARCHAR2(30));

Table created.

SQL> INSERT INTO name_table VALUES(123, 'aligator1234');

1 row created.

SQL>
SQL> CREATE OR REPLACE PROCEDURE tomek
  2  AS
  3    v_id      name_table.id%TYPE      := '123';
  4    v_surname name_table.surname%TYPE := 'aligator1234';
  5  BEGIN
  6    INSERT INTO name_table (id, surname) VALUES (v_id, v_surname);
  7
  8    SELECT id, surname INTO v_id, v_surname FROM name_table;
  9  EXCEPTION
 10    WHEN dup_val_on_index THEN
 11       dbms_output.put_line('value ID=' || v_id || 'value SURNAME=' || v_surname);
 12  END tomek;
 13  /

Procedure created.

SQL> exec tomek
value ID=123value SURNAME=aligator1234

PL/SQL procedure successfully completed.