The files are renamed based on the parent metadata — you can see that if you choose Show File. The attachment title just isn't changed, because there's not much point in duplicating the parent metadata, and site translators can choose titles that make sense based on what's actually being saved. I'd say the real issue here is that triggering the rename operation manually shouldn't update the attachment title.

The attachment title you see in the middle pane isn't the same as the actual filename. When you save from the web, the actual filename is always renamed based on the parent metadata, which you can see if you right-click on the attachment and select Show File.

As I say, there's an inconsistency here in that when you use the manual rename option it also changes the attachment title, but I'm saying that that's the behavior that should probably change, because just repeating the filename in the items list, where you already have the metadata on the parent item, isn't really valuable.

Again, the actual file is renamed — you can verify this yourself with Show File — so you wouldn't see "Full Text" when viewing the PDF. "Full Text" is just the name shown in the middle pane in Zotero itself.

If you're actually seeing "Full Text" in your PDF reader, something is wrong, but that's almost certainly not the case, and if you think it is we'd want to know the exact steps you're taking to reproduce that as well as a screenshot, which you can upload somewhere (e.g., Dropbox) and post a link to here.