score:2
Yes, I guess the most important thing is the name detail written on the "Pay To" column because that's the security mechanism of money order. You also have to keep the receipt because the serial number might help if strange things happened. So it should be ok to leave everything else as blank since your application documents are delivered together with the money order.(I might take a picture before seal the envelop to confirm you put all documents inside) Please also check if they also accept cashier check from any bank in US, that might also be easier for you.