You can assign any name you wish to each of your libraries in the list by first selecting the library, and then clicking on its name to begin editing it (just like renaming a file in the Finder). Alternately, you can control-click on the library and select “Rename Library” from the contextual menu that pops up.
When you first add a library to PowerPhotos, it will be given the same name as the library package has in the Finder. The Finder name and the name in PowerPhotos are separate though, so you can change one without having to change the other. For example, if you’ve added a library that belongs to another user, and that library is named simply “Photos Library”, you can give it a different name in PowerPhotos such as “Bob’s Library” without affecting the name of the actual library on disk.
When renaming a library in PowerPhotos, you have the option to either just change the name as it appears in PowerPhotos, or also change the name of the library on disk at the same time. You can control this setting in the preferences window.
You can also change the name of the library on disk via the Finder. When you bring PowerPhotos to the front, it should see the change and update the path for the library to point at the new location. PowerPhotos will not automatically change its own display name for the library in this case.
If a library shows up in red in the list, it means that the package for that library does not exist on the disk (e.g. it was moved or deleted), 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. If it’s a library that you intentionally deleted or no longer need to access, you can use the “Remove Library” command to remove the library from the list.