How to run update query on multiple table via joins simultaneously on postgres?
I don't see why you would want to do that. Two UPDATE statements in a single transaction will do just fine and won't incur any additional overhead compared to a single statement. 



Having said that: it is possible by using a writeable common table expression

with shape_update as (
  UPDATE prd_shape
   SET name_en = 'Another name'
  WHERE serial_number = '1234ST'
  returning id, serial_number
)
UPDATE prd_sectionshapename 
  SET company_shape_name = 'ABC'
WHERE (shape_id, serial_number) IN (select id, serial_number from shape_update);


That solution indeed has one advantage: you have to specify the value for the serial_number only once. But it has no performance or transactional advantages.