[Vuejs]-Is there a way to pass muttiple values which are not in side a component(dom)?

What you can do is to find in your banks array the ledger_object_type_sub_id who is equal to your bank_name_id.

get_existing_bank_id: function(bank_name_id) {
  console.log(this.banks.find(bank => bank.ledger_object_type_sub_id === bank_name_id).ledger_object_type_sub_name);
}

Here is your fiddle update with the working solution : https://jsfiddle.net/sjh038w9/