You can assign any name you wish to each of your libraries in the list by double clicking on the item and typing in a new name. If you've chosen in the preferences window for double clicking to open the library instead of renaming it, you can rename by option-clicking the library's name instead.

By default, the name you assign here does not affect the name of the folder for the library on the disk, so you can have different names if you wish. You can also check the "Keep library names in sync with folder names" option in the preferences window if you prefer to keep the library name the same as the folder's name. With this option enabled, iPhoto Library Manager will detect a change in either name and update the other name to match.

If a library shows up in red in the list, it means that the folder for that library does not exist on the disk, or the disk the library resides on is not currently available. If the library is kept on another disk, insert or connect the disk, and the library name should change back to black, indicating the library is now available.

See also:

Creating a new library

Adding a library

Removing a library

Duplicating a library

Moving a library