I often open several PDF documents at the same time with okular, and I find it difficult to distinguish between them, looking at the task manager - the problem is, in each control (?) or icon (?), the label only shows the first part of the path of each file. Since they are all somewhere deep in Calibre, I never see the actual file name. Is there any way to edit these labels? (this is plasmashell 5.14.5, on Debian 10)

Why doesn't it show the file name for you? I can't reproduce this problem here, howering on the Okular button in the Task Manager shows the file name for all open PDF, as well as a snapshot image of the currently active page.
FWIW: I use the Icon-only Task Manager, grouping by application, maximum 2 rows.

The problem isn't that it doesn't show the filename, but that it shows the full path - so, since I have my documents/books in Calibre, what I see on the icon/button is something like "/home/user/Calibre Library/Ta..."; hovering doesn't work for me, and any way, I never use that for anything. I would just like to be able to see the short name of the document instead of the start of a full path.

I don't see the full path, I only see the file name. Maybe updating to a newer Plasma version could help in this case...

That is configurable in Okular. Settings->Configure Okular->General tab. There is an option to "Display document title in titlebar if available" and below that, an option to Display the file name instead of the fill path name if the document title is not available.

On my taskbar, the text in a window's icon is the same as the window's titlebar.