Hello...Caina? Well this is an interesting name, but I certainly like it. Hi Caina! :D
Yes, mods can. They can do that by uploading an image into their albums. They must, when creating the album, mark it off as a "profile" album to represent it holding images used for profile decoration. Then they can upload images there, go to the User CP and customize their profile in the fields that allow them to search for album images.
You can try signing your name on it, or you can watermark it...which is essentially just putting your own signature somewhere on your work and lowering the opacity to a certain degree, so if it ever gets stolen there is proof that it does belong to you.