Sometimes the first step to solving your problem is knowing what it’s called. After that, it’s simply a matter of googling. What you are trying to create is called a pivot table or crosstab report. Here is a link explaining how to create pivot tables in MySQL. And here is a more in depth tutorial.

UPDATE:

Now that you’ve updated the question, I have a clearer idea of what you are trying to accomplish. I’ll give you an alternative solution which is similar but not exactly what you want based on MySQL’s GROUP_CONCAT function.

select t1.FirstName, t1.LastName, group_concat(concat(t2.FirstName, ' ', t2.LastName))
from member_information as t1
left outer join member_dependent_information as t2 on t2.MemberID=t1.MemberID
group by t1.MemberID;

I’ve verified this query as follows. First the setup:

create table member_information (
    MemberID int unsigned auto_increment primary key,
    FirstName varchar(32) not null,
    LastName varchar(32) not null
) engine=innodb;

create table member_dependent_information (
    MemberID int unsigned not null,
    FirstName varchar(32) not null,
    LastName varchar(32) not null,
    Type int unsigned not null,
    foreign key (MemberID) references member_information(MemberID)
) engine=innodb;

insert into member_information (MemberID, FirstName, LastName) values
(1, 'John', 'Harris'),
(2, 'Sarah', 'Thompson'),
(3, 'Zack', 'Lewis');

insert into member_dependent_information (MemberID, FirstName, LastName, `Type`) values
(1, 'Amy', 'Harris', 1),
(2, 'Bryan', 'Thompson', 1),
(2, 'Dewey', 'Thompson', 2),
(2, 'Tom', 'Thompson', 2),
(3, 'Harry', 'Lewis', 2),
(3, 'Minka', 'Lewis', 1);

And now the query and results:

mysql> select t1.FirstName, t1.LastName, group_concat(concat(t2.FirstName, ' ', t2.LastName))from member_information as t1
    -> left outer join member_dependent_information as t2 on t2.MemberID=t1.MemberID
    -> group by t1.MemberID;
+-----------+----------+------------------------------------------------------+
| FirstName | LastName | group_concat(concat(t2.FirstName, ' ', t2.LastName)) |
+-----------+----------+------------------------------------------------------+
| John      | Harris   | Amy Harris                                           | 
| Sarah     | Thompson | Bryan Thompson,Dewey Thompson,Tom Thompson           | 
| Zack      | Lewis    | Harry Lewis,Minka Lewis                              | 
+-----------+----------+------------------------------------------------------+
3 rows in set (0.00 sec)