If you want the migrated mapping in Org 2 to use the same object path as in Org 1, you must maintain the same dataset name and table name in the Google BigQuery account for Org 2.
For example, if you have two different accounts, Account1 used for Org 1 and Account2 used for Org 2, the object path for the dataset name and table name must be the same in both the accounts:
Account1: DatasetName1/TableName1
Account2: DatasetName1/TableName1
In this scenario, you do not need to override the dataset and table name in the advanced properties and the mapping runs successfully.