If you were forced to look at the files in the order file 1, file 2, you could store the file 1 data in an hash of arrays, with names as keys. Something like this:

#!/usr/bin/perl 
use strict;
use warnings;

my $fileNameA = $ARGV[0];
my $fileNameB = $ARGV[1];

my %outputHash = ();
my @line;
my $x = 0;

open (my $inputA, "<", $fileNameA);
while (<$inputA>)
    {
        next unless $_ =~ m/\w/;
        @line = split(" ", $_);
        push (@{$outputHash{$line[1]}}, $_);
    }

open (my $inputB, "<", $fileNameB);

while (<$inputB>)
    {
        next unless $_ =~ m/\w/;
        @line = split(" ", $_);
                
        if (exists ${$outputHash{$line[2]}}[0])
            {
                for ($x = 0; $x < @{$outputHash{$line[2]}}; $x += 1)
                    {
                        print STDERR "${$outputHash{$line[2]}}[$x]";
                    }
            }
    }
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But this would only work if the names in file 2 are unique. And it's more efficient to do it the opposite way around if possible, as suggested above.

-Michael