I seconf OriginalGriff's opinion, concatenating first and last name to the same field is a bad idea. As already pointed out store them in separate columns and your operations will be much simpler.
To throw another kind of solution, typically the string after the last space is the last name so in order to find the last name you cuold have something like
SELECT REVERSE( SUBSTRING( REVERSE(FULL_NAME), 0, CHARINDEX (' ', REVERSE(FULL_NAME))))
FROM EMPLOYEE;
But as said, the best option is to store them separately.