Pointing CloudFront URL with different file names to same file

I've files stored in an AWS S3 in the following format

http://ift.tt/1BkNDyO
http://ift.tt/1LVrcdP
http://ift.tt/1BkNFqb

There is also a CloundFront in front of it, so the URLs are like

http://ift.tt/1LVrcdR

The file name "cat.png" is recorded in our own database. We'd like to allow our users to be able to rename files without affecting the existing URLs. So for example, when cat.png is renamed to cat_new.png, (File ID remains same)

http://ift.tt/1LVrcdR
and
http://ift.tt/1BkNFqd

should both work and point to the same file. Is there any way to get this work?

Before we moved to AWS, the file url points to a PHP script, and it will download the same content no matter what the last file name is. It only looks for the account id and file id in URL.