That is the array will need each key that has ch01.03...

If I understand correctly, you have pairs of UID and NAME. There will be several UIDs associated with each name. You want a list of all the unique names and for each name a list of all the UIDs associated with that name. The structure you need for this is a hash of arrays, and you can produce it at the same time you produce your ItemUID hash, as follows:

my %ItemUID = ();
my %ItemName = ();

#Get ItemUID and Item Name (ItemUID is unique to each Test.IData)
{
    my $sql = "SELECT t.IData FROM Tests AS t JOIN Assignments AS a ON
+ a.A
+ssignmentTestID=t.ID JOIN Users AS u ON u.ID=t.UserID WHERE u.Institu
+tionID='004452' AND t.IData REGEXP 'ch01.03.MultipleChoice 049';";

    my $sth = $dbh->prepare($sql);
    $sth->execute();

    while ( my @row = $sth->fetchrow_array() ) {
        my $idata = $row[0];
        while ( $idata =~ /<item([^>]+)/gi ) {
            my $elements = $1;
            my $src;
            my $uid;
            if ( $elements =~ /src=\"\w+\/([^"]+)/i ) { $src = $1 }
            if ( $elements =~ /uid=\"([^"]+)/i ) { $uid = $1 }
            if ( not exists $ItemUID{$uid} ) {
                $ItemUID{$uid} = $src;
                push(@{$ItemName{$src}}, $uid);
            }
        }
    }
    $sth->finish();
}

# you can generate an array of the unique names if you like
my @names = sort keys %ItemNames;
[download]

The hash $ItemName will have keys like 'ch02.03.MultipleChoice 029' and the values will be references to arrays of UIDs.

Hope this helps...