If I understand your problem correctly (my reading is: You have a list of files, you have a list of old/new filename pairs, you want to know which files have a corresponding new filename) then this problem just screams HASH.

A hash lets you index the elements by a string, so rather than searching an array (via List::Compare) for the matching element, you can write things like:

%rename_hash = ( 'oldname' => 'newname' );

if( exists $rename_hash{ $filename } )   # Does this file get changed?
    { ... }

$newname = $rename_hash{ $filename }     # What's the new name?
...
[download]

You might even be able to squeeze all the code into File::Find::find()'s \&wanted parameter (though risky as you'd be changing the data File::Find is looking through).