Can illustrator be exported with an artboard name in front of the file name?

You can alternatively check the "export" tab, where you'll be able to create multiple vrariations of a same artboard in multiple fileformats and sizes, all distributed into their respective folder, with a suffix appended to the original artboard name.
You can also access a similar function for individual assets instead of artboard using the same panel or selecting the elements needed, right click> and choose "collect for export"

in case you just want filename_artboardname, then you can choose to tick the "artboard" and "suffix" when you're do "export as"

However in both cases there is no possibilities to save as an .ai file and separate the artboards by file. You can do it while saving as .svg or .eps though.

Have you checked out "Export for screens" - that is a function in which you can configure artbaord names as part of file names.