Hi @mhuellwegen - great question and ask. I dug in to this and discovered the PDF document should have the Title metadata set. Afterwards, a browser (not just Edge Insider) will use it for rendering the tab title.
In short, the PDF author/creator needs to set the data field. Via Acrobat Pro, open the PDF and select File -> Properties -> Description and then edit the metadata title.
Before i've posted my suggestion, i double checked this "missing" behavior on MS Edge (44.17763.1.0).
While e.g. Chrome (74.0.3729.169) does it best "TitleOnly" as Tab-Label, i realised that my MS Edge Browser does not care about the "MetaTitle" in the metadata of the PDF, also not, if the title is proper set with Acrobat or a PDF library.
By the way, Firefox (66.0.3) showing both in the Format "Title - and Filename.pdf" as Tab-Label, what i think is to much.
There is a little workaround for MS Edge: If the source for the PDF is an URL to e.g. an ASPX-Script, MS Edge make use of the last Folders name (the last part of the URL before Parameters, assuming this is the PDFs filename) for rendering the tab title, while behind this szenario a default.aspx script (not mentioned in the URL) delivers the PDF. So you can Play with the last Folders Name as a propper title.
By the way, extra URL Parameters behind a "?" are also ignored for rendering the tab title.