Oracle Backup/Recovery architecture
With a modern release (>= 10g) and the usage of a Recovery Area (DB_RECOVERY_FILE_DEST is set), the initialization parameter DB_UNIQUE_NAME (derived from DB_NAME if not specified explicitly) tells RMAN in what subdirectory of the Recovery Area the controlfile autobackup must be searched for.
Without usage of Recovery Area, and in status NOMOUNT (no controlfile is opened), you must set DBID for RMAN in order to enable it to retrieve the right controlfile autobackup.