sorry for answering my own question :-) , but I just found something that works :
I was reading this, since it's the component uses the same js if I'm not mistaken (quite clearly mentionned in its name)
https://stackoverflow.com/questions/24457064/mozilla-pdf-js-how-to-i-specify-the-filename-for-download
so I tried the suggested answer, which is to make sure the URL looks like this
http://domain.com/path/to/your/api?fileId=123&saveName=Named.pdf
So for us, we just added &saveName=FileName, which works perfectly to download FileName.pdf instead of document.pdf
"/KZ_FileCache_CS/rest/FileStorage/GetFile?Id=" + FileCache_Create.FileCacheId + "&saveName=" + FileName
