If I read you correctly, that’s going to be a function of your browser and/or OS. (That is, if you are uploading a JPEG image into an attachment field and then saving — downloading — that image to local storage, changing the name in the process.)
One possibility is that you aren’t giving the renamed file a valid extension — for instance, if you are saving 'design.jpg' as 'test' rather than 'test.jpg'. (If you’re using a flavor of Windows, its default setting ‘helpfully’ hides file extensions on known file types, so the only visible difference between 'test' and 'test.jpg' when stored on your local drive is that the computer can’t open 'test' as an image.)
If you are uploading 'test.jpg' to an attachment field and then using a formula field to rejigger the URL, thus changing the file name: You can’t. The name of the uploaded file can’t be changed…
