Perhaps use a scalar to keep track of whether you've seen the first line:

my @ODB;
my $firstLine++;
open (ORGDB, $database) || die "open $database -$!\n";
while (<ORGDB>) {
   next if ($firstLine);
   push (@ODB, $_);
   $firstLine = '';
}
close (ORGDB)
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Or if you can be sure that first line will not change:

my @ODB;
open (ORGDB, $database) || die "open $database - $!\n";
while (<ORGDB>) {
   next if (substr($_, 0, 12) eq 'company_name');
   push (@ODB, $_);
}
close (ORGDB);
[download]