Unfortunately this isn't a feature in web browsers anymore. Years ago you could use a JavaScript routine to disable this but that just causes other issues now.
The best solution, in my opinion, is to watermark your pictures before you upload them. Then if someone copies them your 'name' will always be on them. Choose a good watermark 'signature' that doesn't cover up the meaning of the image but shows that you are the owner. Some watermarks are transparent. meaning you can see them on the image but they also show the background through the watermark so you are not losing the message of the image.
You may have to play around a bit with this to get the watermark you like but it is doable.
-Mark
