MySQL select with CONCAT condition

The aliases you give are for the output of the query - they are not available within the query itself.

You can either repeat the expression:

SELECT neededfield, CONCAT(firstname, ' ', lastname) as firstlast 
FROM users
WHERE CONCAT(firstname, ' ', lastname) = "Bob Michael Jones"

or wrap the query

SELECT * FROM (
  SELECT neededfield, CONCAT(firstname, ' ', lastname) as firstlast 
  FROM users) base 
WHERE firstLast = "Bob Michael Jones"

Try this:

SELECT * 
  FROM  (
        SELECT neededfield, CONCAT(firstname, ' ', lastname) as firstlast 
        FROM users 
    ) a
WHERE firstlast = "Bob Michael Jones"

SELECT needefield, CONCAT(firstname, ' ',lastname) as firstlast 
FROM users 
WHERE CONCAT(firstname, ' ', lastname) = "Bob Michael Jones"