It's not clear what you're trying to secure against. Are you worried about securing a particular image so that only certain designated users can see it? Are you worried about the original name "leaking"? Are you worried about someone iterating through all of your images?

In general, relying on a "secret" URL is not a good way to keep things secret. Google has a nasty habit of finding URLs you thought had no links. Definitely tune your robots.txt to keep the images off legit search engines.