Not sure I understand your question. On Oracle 11 each database's DB_UNIQUE_NAME must be different or the databases will not communicate.
You can check the V$DATABASE view to get the DB_UNIQUE_NAME.
Data Guard Concepts and Administration is a great source of information on this:
It has unique value on the primary database and on each standby database(s).
So on the Primary it can be different that the DB_NAME as long as its unique.
Also of interest:
Unable To Start Oracle Restart Db using 12c if db_unique_name and db_name are different [ID 1479564.1]
11.2 Data Guard Physical Standby Switchover Best Practices using the Broker [ID 1305019.1]