Shoebox catalogs store the path to each photo. If you rename or move a photo in the Finder, Shoebox won't know where to find it. However, there are a number of ways to rename and move photos using Shoebox.
To rename a photo, double-click its name in list view.
Moving Your Pictures Folder
Each Shoebox catalog has a "pictures folder" where most of its photos are stored. The default is ~/Pictures, but you can choose a different folder in the Catalog preferences. Shoebox stores the relative path for each photo inside the folder, and the absolute path of each photo outside the folder.
It's easy to move your pictures folder to a different folder, or a different disk. After you've moved the folder, just open Catalog preferences and select it as your new pictures folder.
If you'd like to move your catalog to a different computer, first copy the file ~/Library/Application Support/Shoebox/Photos.shoebox to the same location on the new computer. Then, copy your pictures and select the correct pictures folder.
Moving Photos in Shoebox
To move the selected photos to a different folder, choose Photos ▶ Move/Copy ▶ Move to Folder, and choose a folder. To move more photos to the same folder, choose Photos ▶ Move/Copy ▶ Move to “Recent Folder” (⎇⌘M).
After you have added all your photos to categories, your existing folder structure becomes less relevant. Rather, it may be more convenient to just organize all your photos into folders by date. To do so, choose Photos ▶ Move/Copy ▶ Move to Shoebox Folder. For example, a photo taken on February 25, 2005 will be moved to ~/Pictures/Shoebox/2005/02/25.
Moving Photos in the Finder
It's possible to move photos in the Finder too. An invisible file in each folder stores the categories for each photo. If you move a folder (as opposed to individual photos), connections in Shoebox will break—but it's possible to restore them. Choose File ▶ Utilities ▶ Reconnect Categories to Photos, and then choose a folder. All the photos in the chosen folder will be added back to their categories.
However, this may result in duplicate photos in the catalog: a missing photo at the old location, and a good photo at the new location. To remove all the references to missing photos, choose File ▶ Utilities ▶ Remove Missing Photos from Catalog.