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

my $path = "/some/path";
my $name = "name";
my $start = "$path/080801_$name";
my $end = "$path/080930_$name";

for my $file (grep {$_ ge $start && $_ le $end} glob "$path/??????_$name") {
	open my $fh, "<", $file or die "unable to open $file";
	while (<$fh>) {
		# process...
	}
	close $fh or die "unable to close $file";
}