From the navigation bar at the top of your album, select the "albums & upload" tab."
Click on the thumbnail for the image that you would like to rename.
On the bottom left corner of the full size page, click on the "rename" link next to your existing filename.
Add a new name for your content into the field.
Click on the "ok" button when you are satisfied with your entry.
A message will pop up that explains that changing the filename of your content will break all existing links to it. If you still want to proceed, click on the 'OK' button, or 'Cancel' to leave your filename unchanged.
A "File renamed" message will appear at the top of your page.
Your new filename will now be visible inside of your Photobucket account.