The image is associated with the product by its content guid, which is permanent. What you can do is probably this (pseudo untested code)

var contentLink = product.CommerceMediaCollection.First().AssetLink;

var media = contentRepository.Get<MediaData>(contentLink);

media.Name = "Can I actually do this";

contentRepository.Save(media, SaveAction.Publish, AccessLevel.None);

This is pretty close. You'll also want to update the RouteSegment value to show the updated name in the image url, and before you do anything create a writeable clone as the object returned by the repository will be read only.  So something like;

var contentLink = product.CommerceMediaCollection.First().AssetLink;

var media = contentRepository.Get<MediaData>(contentLink);

var mediaClone = (ImageData)media.CreateWritableClone()

mediaClone.Name = "Can I actually do this";

mediaClone.RouteSegment = "Can I also do this"

contentRepository.Save(mediaClone, SaveAction.Publish, AccessLevel.None);

Thanks Quan and David