Hi
This is a quick setup that seems to work:
import rhinoscriptsyntax as rs
import os
objects = rs.GetObjects("Select objects to export", 16)
for obj in objects:
name = rs.ObjectName(obj)
stl_suffix = '_{}.stl'.format(name)
stl_basename = rs.DocumentName().split('.')[0]
stl_fullname = '{}{}'.format(stl_basename,stl_suffix)
stl_path = rs.DocumentPath()
full_filepath = os.path.join(stl_path,stl_fullname)
rs.SelectObject(obj)
command_string = '-_Export "{}" _Enter _Enter'.format(full_filepath)
rs.Command(command_string)