You need to use our $my_variable_name; You may thing hardcoding the name is a problem, but it's not. The only reason you need our is because you hardcoded the name in the print. For example,

use strict;
use warnings;

package Hack;

sub slash {
   my $var_ref = do { no strict 'refs'; \${'ExistingPackage::var'} };
   $$var_ref = 'bar';
}


package main;

ExistingPackage->print_it();
Hack->slash();
ExistingPackage->print_it();
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use strict;
use warnings;

package ExistingPackage;

our $var = 'foo';

sub print_it {
   print("$var\n");
}

1;
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package ExistingPackage;

$var = 'foo';

sub print_it {
   print("$var\n");
}

1;
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yes but imagine the following situation

include_file.pl (this is the only file I can edit)

my $test="my_variable_name";  # I pulled this from the db.  I have no 
+idea what it actually is, plus I need to be able to support arbitrary
+ additions to the db anyway
my $default_value="the value I set";
$$test = $default_value;
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module.pm (I can't touch this file)

use strict;
package apackage;
do "include_file.pl";
print "the value of \$my_variable_name = $my_variable_name\n"; # I can
+'t control the fact that this variable is being referred to without i
+ts package name
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script.pl (this is the code that will be run. I also can't touch it)

use strict;
use module;
$my_variable_name = "A new value";
print "the value of \$my_variable_name = $my_variable_name\n"; #print 
+the local value
print "the value of the package variable = $apackage::my_variable_name
+\n"; # print the package value
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The question is how do I while only modifying the include file avoid failing use strict. While still allowing the module file to access the variable by name directly and the script file to access it by package.

There more than one kind of strict errors. Undeclared variables will lead to strict errors. my and our help fix these errors. However, the error in include_file.pl is not caused by undeclared variables. It's caused by using symbolic references. It's possible to write code that fetches a reference to a symbol while being strict-friendly, but it's much simple to temporarily disable checks for symbolic references. That can be done as follows:

# include_file.pl

# Pulled from the DB.
my $test          = "my_variable_name";
my $default_value = "the value I set";

my $var_ref = do { no strict 'refs'; \${$test} };

$$var_ref = $default_value;
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By the way, script.pl doesn't compile. I'm going to assume your real script.pl doesn't have that problem.

Hrm. Note where I declare vars:

package apackage;
my $test="my_variable_name";
my $default_value="the value I set";
$$test = $default_value;
print "the value of \$my_variable_name = $my_variable_name\n";

package main;
$my_variable_name = "A new value";
our $test;
print "the value of \$my_variable_name = $my_variable_name\n";
print "the value of the package variable = $apackage::my_variable_name
+\n";
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Yields:

the value of $my_variable_name = the value I set
the value of $my_variable_name = A new value
the value of the package variable = the value I set
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$/  =  q#(\w)#  ;  sub  sig { print scalar reverse  join  ' ',  @_  } 
+ sig
map { s$\$/\$/$\$2\$1$g && $_ } split( ' ', ",erckha rlPe erthnoa stJu
+" );
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