Welcome to the Monastery (and be not offended; many new monks have had a first post get that for an initial answer).

But we'll likely be more helpful if you:

1. Post the script you've tried, along with an explanation of how (error messages, warnings, unexpected or no output) it fails to do what you want.
2. Be a bit more specific about your data: are the source files text (free text), CSV, out of a DB or what.
3. Read How do I post a question effectively? and Markup in the Monastery

If you haven't written any code yet, you might want to think about these semi-random observations:

• Do you have enough RAM to read "~ 100,000 rows" (x 2 ???) into memory at once? That may determine the manner in which you proceed.
• If you're just starting Perl and have no programming experience, you may need to tackle simpler tasks before tackling this one. In that case, you're in the right place: see Tutorials, use Super Search and consider a book such as Learning Perl.

Use a hash to store all lines of the ID file with Catg_ID as key and the other values as data (as a string "12 16"). This should hopefully still fit into memory, if not use something like DMB::Deep to store the hash on disk

Then just read the Name file line by line, check for the ID in the hash and compare.

#!/usr/bin/perl

use strict;

my $data_1 = <<EOF;
ID Catg_ID Pos
12 A 16
15 B 5
16 A 175
EOF

my %record;
open( my $file_1, "<", \$data_1 )
  or die "Cannot open data_1\n";

while (<$file_1>) {
    next if ( /^ID/ );
    s/(\d+)\s//;
    $record{$1} = [ split ];
}

while (<DATA>) {
    next if ( /^Catg/ );
    my @cols = split;
    for my $i ( keys %record ) {
        print "$i $cols[0] $record{$i}->[1] $cols[3]\n"
          if (( $record{$i}->[0] eq $cols[0] )
          && ( $record{$i}->[1] > $cols[1] )
          && ( $record{$i}->[1] < $cols[2] ))
    }
}
__DATA__
Catg_Name Start Stop Name
A 8 19 jamm
A 110 112 bbc
E 170 256 vadd
A 14 18 cip
[download]

Thank you bichonfrise74. Your suggestion works very well. It is much simpiler and quite a bit faster than what I was using:

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

my $idfile = 'C:...';
open(ID, $idfile) or die "Cannot open file '$idfile' \n\n";

 #Create and open output file
my $out = 'C:\Users\Clayton\Documents\Research\GO\Data\chr_8\chr_8_pos
+gen';
open (OUT, ">$out");

# Create Variables
my $line;
my $line2;
my %hash = ();

# Read in file line by line
while ( $line = <ID> ) {
    chomp $line;
    # Split the tab delimited file into an array
    my @arr = split /\t/, $line;
    #if(defined($arr[2])){
    # Put the columns of the array into variables
    my $id = $arr[0];
    my $catg_id = $arr[1];
    my $pos = $arr[2];
    
    $hash{$id} = "$catg_id\t$pos";
    
}
close ID;

my @k = keys %hash;
my $k;

my $namefile = 'C:...';
open(NAMEFILE, $namefile) or die "Cannot open file '$namefile' \n\n";

while ( $line2 = <NAMEFILE> ) {
    chomp $line2;
    
    my @loc = split /\t/, $line2;
    
    foreach $k (@k) {
        my @arr2 = split /\t/, $hash{$k};
        if($loc[0] == $arr2[0]){
            if(($arr2[1] >= $loc[1]) and ($arr2[1] <= $loc[2])){
                print OUT "$arr2[0]\t$k\t$arr2[1]\t$loc[1]\t$loc[2]\t$
+loc[3]\n"
            
}}}}
[download]

I'm still new to perl so I guess a lot of my methods are not the most efficient.

One more question though... Whenever I use your code or mine I get an error "Use of uninitialized value in numeric gt (>)at C:\...line 32, <NAMEFILE> line 1. This error repeats many times for each line in the file. The output is what I expect it to be though and the program runs without any problems (other than generating a bunch of warnings).

You should eliminate the warnings since they may indicate bugs in your code. I do not know which line is line # 32, but perhaps you could try to determine the cause of the warnings by printing the contents of your @loc and @arr2 arrays. Do they have as many elements as you think they have?