I save files as PDF often from QB and the solution is relatively simple, at least in my experience.

When you save as pdf you should be prompted for a location and, of course, the suggested name is i the location box.  Can't you overwrite the name when you save it? You certainly can determine the location to be different than what QB suggests as a default.

If that fails, the other option is to Print to PDF, which allows you to choose your own name as well as location.  All you need is an installed PDF Printer. If you do not have one already might I suggest BullZip  - I use it all the time with never an issue. You can choose to open the pdf when it is created and from (usually Adobe) pdf viewer you can direct print a hard copy