how to concat two columns into one with the existing column name in mysql?

As aziz-shaikh has pointed out, there is no way to suppress an individual column from the * directive, however you might be able to use the following hack:

SELECT CONCAT(c.FIRSTNAME, ',', c.LASTNAME) AS FIRSTNAME,
       c.*
FROM   `customer` c;

Doing this will cause the second occurrence of the FIRSTNAME column to adopt the alias FIRSTNAME_1 so you should be able to safely address your customised FIRSTNAME column. You need to alias the table because * in any position other than at the start will fail if not aliased.

Hope that helps!

Instead of getting all the table columns using * in your sql statement, you use to specify the table columns you need.

You can use the SQL statement something like:

SELECT CONCAT(FIRSTNAME, ' ', LASTNAME) AS FIRSTNAME FROM customer;

BTW, why couldn't you use FullName instead of FirstName? Like this:

SELECT CONCAT(FIRSTNAME, ' ', LASTNAME) AS 'CUSTOMER NAME' FROM customer;