Insert query in mysql
You could do something like:

INSERT INTO test_table
    (first_name,last_name,full_name)
SELECT first_name,last_name
     , CONCAT(coalesce(first_name,''),coalesce(last_name,''))
FROM (
    SELECT 'raju' as FIRST_NAME
          ,'pydi' as LAST_NAME
) AS T;


I still think it's a pretty bad idea to store full_name though. You could create a view like:

CREATE VIEW TEST_VIEW AS (
    SELECT first_name, last_name
         , CONCAT(coalesce(first_name,''),coalesce(last_name,'')) as full_name
    FROM test_table
);