You can access this menu option by right-clicking an image. So why would you want to save your image to a new file name?
The most common reason would be to save a resized image to a new file name and make the resized dimensions permanent. Let's say you took a screenshot of the desktop by pressing PrtScrn. Then you paste it into the editor. Fast-Help needs to save this image, so it makes a name for it, something like "Image12345.jpg" and saves it to your Images folder. But it's too big, so you select it, grab the resize handle in the bottom right corner and resize it to a more useable size.
But when you resize an image, you don't actually change its original dimensions, you merely change how it appears within the editor. So your screenshot could be a 1.5mb file, but resized it doesn't look like it should take up much room, but it still takes up 1.5mb. That's where this screen comes in. Saving it to a new file name will make those resized dimensions the new dimensions, vastly reducing the image size.
You may also like to convert the image format, for example, save a bitmap as a JPG image etc.
Just type in your new unique file name, select the new File Type option and click OK. Your new image will be automatically inserted for you, replacing the previous one.
You can optionally choose to delete the original image by checking the Delete box.