Am I not already saving 'rescaledRaster' with rescaledRaster.save(outName)? I've tried the following as well, which is what I think you're suggesting:
name = inRaster.name.replace('Int_Raster','Resc')
rescaledRaster.save()
arcpy.Rename_management(rescaledRaster, name)
I've done it with and without the following addition beforehand, as per this thread.
arcpy.env.overwriteOutput=True
if arcpy.Exists(outName):
arcpy.Delete_management(outName)
I get the following error message regardless:
arcgisscripting.ExecuteError: ERROR 999999: Error executing function.
The table already exists. [name]
Failed to execute (Rename).
("name" is the actual name, not the variable). I cannot do
arcpy.Rename_management(rescaledRaster, outName)
or else I get this:
ERROR 000670: output Output Data is same as input Input Data Element