When I direct connect my laptop to these drives via a USB hub, the drives and their folders appear as a different name
I understand why the drives would show up as a different name; I am not understanding why the folders appear as a different name.
I can still see the drive designations but Windows will not access them (denied permission even though those same drives allow access through WiFi).
This is a Windows issue, you'd need to change the permissions in Windows. Once you are able to access the photos, you should be able to make use of them in Lightroom, you'd have to reconnect the photos using these instructions: Adobe Lightroom - Find moved or missing files and folders
Sorry. The individual folders within the drives do retain the same name regardless of how the drives are labelled. When direct connected through USB, drives carry their names (Seagate...) along with a letter designation. Then, subfolders (photos/2016/Feb 2016) carry the name with them (e:\photos....) etc.
I realize this is a Windows issue but haven't been able to find help there. This only affects Lightroom. In PS Elements, for example, the same photos show up regardless of network designations.
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If the drive letter changes, you can force the drive letter to be the same no matter how you connect. This is a Windows function. Change, add, or remove a drive letter - Windows Help
Or, as I said, you can reconnect the catalog in Lightroom using the link I gave in my previous message.