Hi Raphael,
The Title and many other fields in the PDF properties are controlled in InDesign by File > File Info.
I don’t know any way to automatically populate the File Info dialog box with the document name like that. (In most cases, you would NOT want the document title to be in the PDF metadata… but I can see why you do want it in this situation!)
So I did find some old scripts (which didn’t work on CC 2015) to do this — seems I’m not alone in this request but I solved it by creating a macro with my Microsoft keyboard!
If you are in indd, press shortcut CTRL+WIN+SHIFT+E – Macro takes name of file without extension. Then open info dialog and insert the name in Title box.
I have CZECH version, but i think it should be work in other languages too.