MySQL - Set default value for field as a string concatenation function

MySQL does not support computed columns or expressions in the DEFAULT option of a column definition.

You can do this in a trigger (MySQL 5.0 or greater required):

CREATE TRIGGER format_stage_name 
BEFORE INSERT ON actors
FOR EACH ROW
BEGIN
  SET NEW.stage_name = CONCAT(NEW.forename, ' ', NEW.surname);
END

You may also want to create a similar trigger BEFORE UPDATE.

Watch out for NULL in forename and surname, because concat of a NULL with any other string produces a NULL. Use COALESCE() on each column or on the concatenated string as appropriate.

edit: The following example sets stage_name only if it's NULL. Otherwise you can specify the stage_name in your INSERT statement, and it'll be preserved.

CREATE TRIGGER format_stage_name 
BEFORE INSERT ON actors
FOR EACH ROW
BEGIN
  IF (NEW.stage_name IS NULL) THEN
    SET NEW.stage_name = CONCAT(NEW.forename, ' ', NEW.surname);
  END IF;
END

According to 10.1.4. Data Type Default Values no, you can't do that. You can only use a constant or CURRENT_TIMESTAMP.

OTOH if you're pretty up-to-date, you could probably use a trigger to accomplish the same thing.