Jerry, when you copy/paste an image or add an effect (like a drop-shadow), that's when VSD saves the image as IMG_#.jpg.
When I start a site I create a folder for images and one for graphics. When I'm working on the site – moving things around, etc. I don't worry about those 'generic' jpeg files, but when I have things the way I want them, I delete those images and then insert the original image from its folder. So (for example) I would delete "IMG_14.jpg" and insert "my_dog.jpg". If this is a photo or graphic that gets replaced often (like a special or sale), I delete that item from the site and the Files folder, then add the new item from the images/graphics folder.
You can go to your site online and right-click images to see what IMG number they are so you know what to delete, then replace it with the original image.

If you delete the unused IMG_#.jpgs out of the Files folder, you won't have to worry about old stuff showing up when you make changes to the site.

I hope that makes sense

@ Eric, thank you very much for that code. I used the "Edit Header" function from the "Edit" menu to enter your no cache code. It isn't working. And, now that I've experimented with your idea, I see that the problem actually still exists on other browsers as well as the Facebook browser, too.

@ Inger, Thank you! I didn't exactly understand that when I first came on this forum, until I read some of JoAnn's remarks. I do thank you and her for all of you for your input!

@ paintbrush, That kind of makes sense. I may have to explore it. It seems a bit complicated. I don't have time at this very moment to see how that works, but I will look into it when I have more time. I just thought I was stuck with whatever names VSD decided to name my images. I should be able to investigate it tomorrow. Thank you!