There's nothing inside your "while" loop that changes the value of $GetName, yet every iteration of your loop checks whether the value of $GetName contains an open paren. You could just check for this once, before going into the loop.

The inner "for" loop checks whether the numbers "1" through "12" occur in the current file name, but the way you're doing it, a file name containing "21" will match on two iterations (because it contains "1" and "2") and a name containing "1123" will match five times ("1", "2", "3", "11" and"12").

There seems to be a dependency between the value of $GetName and the values of $StartCh and $EndCh, but I'm not sure how these are related, exactly. If you can clear that up, things might make more sense.

If you are dealing with file names that use fixed-width digit strings with leading zeros, you might want to use a regex that checks for a specific number of digits between non-digit characters -- for example, if you're looking for file names in the range "test_0001.txt" through "test_0012.txt":

my $digit_width = 4;
my $min = 1;
my $max = 12;
my $prefix = "test_";
my $ext = ".txt";

while ( my $file = readdir DIR ) {
    next unless ( $file =~ /^ $prefix (\d{$digit_width}) $ext $/x );
    if ( $1 >= $min and $1 <= $max ) {
        # we have a match... now what?
    }
}
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Yes there is a dependency on the $GetName value because that is what the user is going to input for the program to use as a search criteria when it scans the directory for files. The $StarCh and $EndCh are basically chapter numbers. starting and ending chapters. Each of these files that will be in the directory The files will have the chapter number within the file name somewhere. For example "Test_001.txt" will be chapter 1 file but depending on who created the files, someone could have a totally different naming convention such as "Ch 1 title 3rd edition". Something like this will throw off my whole program and thats where I need the program to be more robust. I need code to handle many possibilities. Now thinking about it, maybe there isnt a way for to actually code all possibilties. Thanks for your input and some of your suggestions does help me for what its worth. Thanks!

Using your code:
my $digit_width = 4; # This isnt necessarily true every time
my $min = 1;
my $max = 12;
my $prefix = "test_";
my $ext = ".txt";

while ( my $file = readdir DIR ) {
    next unless ( $file =~ /^ $prefix (\d{$digit_width}) $ext $/x );
    if ( $1 >= $min and $1 <= $max ) {
        # we have a match... now now we want to create the new file na
+me
        # Whatever $SetName was so if $SetName = "Chapter \1" which me
+ans 
        # The new file name for the program to modify in the directory
+ is 
        # to "Chapter 01.txt" for the 1st chapter file which wouldve b
+een
        # Test_001.txt in the directory it searched in. I will then
        # have the code rename the file.
    }
}
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Unterminated <> operator
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The following:

... and $orig_cnt=1)
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is an assignment. It should probably be a numeric check (==):

... and $orig_cnt==1)
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I also see that in two other places in your code.

Other advice:

• use strict and warnings
• perlcritic is a tool which can help you make your code more robust.

I did notice however a curious string: "Chapter \1". It made me wonder what you want to do with the ctrl-A, aka "SOH" character. But then I noticed it's assigned to a variable that isn't further used.

Yes the string "Chapter \1" is a string I would get from an textbox which the user inputs this text, the backslash is suppose to be a real backslash so maybe the string probably should look like this: "Chapter \\1" perhaps.

Similarly,
print "$file does not match\n";
could be modified to
print "'$file' does not match '$subname'\n";