Hello perly_white, and welcome to the Monastery!

The requirements are not entirely clear. If filenames can appear out-of-order in the input file:

Filename1 Item1 - Answer
Filename2 Item1 - Answer
Filename1 Item2 - Answer
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then you will need to either (1) read the whole file into a suitable data structure before writing tables, or (2) keep track of each open file, associating the filename with the handle. For (1), you could use a hash of arrays¹ like this:

my %files;
$files{Filename1} = [ 'Item1 - Answer' ];
push @{ $files{Filename1} }, 'Item2 - Answer';
...
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For (2), you would need a simple hash with filename/filehandle key/value pairs.

However, it appears from the question that you know in advance that filenames cannot appear out-of-order. If that’s the case, the following skeleton script should provide a straightforward approach:

use strict;
use warnings;
use autodie;

# open the data file for reading
my $data_filename = 'data.txt';
open my $in_fh, '<', $data_filename;

# output files
my $current_filename = '';
my $out_fh;

while (<$in_fh>)    # process one line of data
{
    my ($new_filename, $item) = split ' ', $_, 2;

    if ($new_filename ne $current_filename)
    {
        finalize_table($out_fh) if defined $out_fh;
        open $out_fh, '>',  $new_filename;
        $current_filename = $new_filename;
        initialize_table($out_fh);
    }

    add_row($out_fh, $item);
}

close $in_fh;

finalize_table($out_fh) if defined $out_fh;

sub initialize_table { ... }

sub add_row          { ... }

sub finalize_table
{
    my ($fh) = @_;
    # ...
    close $out_fh;
}
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Update: ¹See perldsc#HASHES-OF-ARRAYS.

Hope that helps,