DROP FUNCTION IF EXISTS PersonName;
DELIMITER |;

CREATE FUNCTION PersonName( personID SMALLINT )
RETURNS CHAR(20)
BEGIN
  DECLARE pname CHAR(20) DEFAULT '';
  SELECT name INTO pname FROM family WHERE ID=personID;
  RETURN pname;
END;
|
DELIMITER ;

...
END
|
DELIMITER ;

DELIMITER |;

DELIMITER |

DELIMITER ;

DROP FUNCTION IF EXISTS PersonName;
DELIMITER |

CREATE FUNCTION PersonName( personID SMALLINT )
RETURNS CHAR(20)
BEGIN
  DECLARE pname CHAR(20) DEFAULT '';
  SELECT name INTO pname FROM family WHERE ID=personID;
  RETURN pname;
END
|
DELIMITER ;

DROP FUNCTION IF EXISTS PersonName;
DELIMITER |

CREATE FUNCTION PersonName( personID SMALLINT )
RETURNS CHAR(20)
BEGIN
  DECLARE pname CHAR(20) DEFAULT '';
  SELECT name INTO pname FROM family WHERE ID=personID;
  RETURN pname;
END;
|
DELIMITER ; /* <-- add a space between DELIMITER and the semicolon */

DELIMITER ;