Is it possible to change the Font properties of Show_Name?
Not quite sure what you mean. Show_name is a boolean, so it’s either true or false. If you mean change the font used for the object’s name on screen, then no, I don’t think so. It uses the same font as the rest of the UI. You can, however, change the font of the UI.
It’s quite possible if you want to get into bgl and overlay a custom font as modal operation.