How does Recovery Catalog Recognize Databases Which is Which?

Normally and generally, recovery catalog recognizes the databases by DBID which is a unique number among different databases. But there's a problem: the primary database and its standby databases share the same DBID, this could make the standby database sync its meta data back to the recovery catalog. This is the source of our problem.

When the primary database tries to perform a backup, it will find out its meta data is different from the catalog and asks for DBA's intervention before doing any further backup. In such case, you can perform a crosscheck to work around it.
RMAN> crosscheck archivelog all;
For resolving the confusion, Oracle uses a new parameter called DB_UNIQUE_NAME since 10g onward to distinguish the databases that share the same DBID. More examples can be found in the following link:
12 Using RMAN to Back Up and Restore Files