There's an awesome and often unused tool that comes with perldoc that will just tell you about particular Perl keywords. Using "perldoc -q my" will tell you that,

 A "my" declares the listed variables to be local (lexically) to the e
+nclosing block...
[download]

So, enclosing your variable declarations inside of different blocks resolves the problem. Here's a more involved example:

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

package Foo;
{
my $package = __PACKAGE__;

sub new {
    return bless {'PACKAGE'=>$package}
}

}
package Bar;
{

my $package = __PACKAGE__;

sub new {
    return bless {'PACKAGE'=>$package}
}

}

package main;

my $foo = Foo->new;
my $bar = Bar->new;
print $foo->{'PACKAGE'};
print qq|\n\n|;
print $bar->{'PACKAGE'};
[download]

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