I was wondering if it was possible to batch rename objects with python, while still keeping a basic naming convention intact.
I have no idea what you mean by "basic naming convention". There is no such a thing for all I know, but you can rename objects with Python in Blender any way you can possibly imagine.
For example if I wanted to name all selected objects that are in the negative x side "Left" and all objects in the positive x side "Right" I could execute this in the text editor:
import bpy for o in bpy.context.selected_objects: lx = o.location.x o.name = "Left " * (lx<0) + "Right " * (lx>0) + o.name
It doesn't need to be this simple - you can program any naming rules and conditions you can imagine with Pyhton. If you need help with this, Blender Stack Exchange is a great place to get it - just ask a more specific question.