This script is meant to be running from the Maya script editor, it will then edit the workspace file by itself.
The problem is, that Scenes get renamed a lot (save as, increment save, etc), so wanting to have the Scenename as folder means that this would have to be run right before a scene is rendered:
import maya.cmds as mc
#get file path
fn = mc.file(q= True, sn = True)
#get Scene Name
fn = fn.split("/")[-1]
fn = fn.split(".")[0]
renderpath = "../RENDER/{1}".format(fn)
#set imagepath variable in workspace
mc.workspace(fr = ['images', renderpath])
I took out everything that changes location back, since this seems to be an inhouse tool. Also I realised that the workspace file allows relative pathing.
So if you add this script to a shelf button, that needs to be pressed before rendering, it should work fine.
You also could start the render directly in the script, and just make it the "start render" button of your studio.
If you want to be more automated, you could also format it in a function and add it to userSetup.py:
def imagePath():
#get file path
fn = mc.file(q= True, sn = True)
#get Scene Name
fn = fn.split("/")[-1]
fn = fn.split(".")[0]
renderpath = "../RENDER/{1}".format(fn)
#set imagepath variable in workspace
mc.workspace(fr = ['images', renderpath])
along with a protected scriptjob that runs this command whenever a file is saved.
Now there is also a less hacky way to do this using the interface:
Since the workspace accepts relative pathing you could just change the render image path in File>Project Window to "../Render"

Sadly I couldn't find a keyword that just grabs the scene name for the workspace pathing. Maybe there is one but I haven't found it yet.
But some Renderers like Arnold also allow for relative Pathing, with this and Arnold you could just use the <Scene> keyword in the render Settings.

This is ofcourse different from Renderer to Renderer, but if you know if you the Renderer you use allows this, you could also solve it like this.
I hope it helps!