In some special cases (for example, setting your site's logo and header image) it can be very important that the image used on your site has the correct name. However, it can be confusing to determine whether an image has been renamed correctly.
The easiest way to rename an image is through the Contents view.
In the Contents view, you can find your image and click the checkbox next to it to select it.
Next, scroll down to the bottom of the page and click the Rename button.
When renaming an image, the important property is the Short Name. This name is what shows up in the URL when you navigate to the image. This is also the name that the site looks at to determine whether the image is a site logo or header image. As you can see below, the selected image is correctly named such that its Short Name and Title match. While this isn't necessary, it's strongly recommended. The Short Name will only be seen here and in the URL, while the Title will be used everywhere else, so having different names could potentially cause confusion.
After you've chosen a new name for your image, click Rename All to update it.