None that I know of.
Sounds like a nightmare.
Assuming you mean that image X would be accessed by abcde.jpg until you generated a new code, and then that link would be invalid and it would be accessed by fghij.jpg
Lots of 404 not founds.
Well, you could use Photobucket. Create an album "314159". Place your images there. When you want to change the URL of an image, move the image to another album "141421", which will change the link. If you want the old links to remain valid, copy the image to the new album.
Wash, rinse, repeat.
I imagine that you could do similar on other image hosting services.
Not sure how happy the service would be with you doing this trick.
Why would you want such a service? A form of hotlink protection?