The database administrator (DBA) is the Linux user account that owns the database catalog and data storage on disk. The DBA can bypass all database authorization rules. However, the DBA must supply a password to connect to a running database and to use Administration Tools commands that affect a running database. The DBA can drop a stopped database without supplying a password.
A database is a 
cluster of nodes that, when active, can perform distributed data storage and SQL statement execution through administrative, interactive, and programmatic user interfaces.
A cluster generally refers a collection of hosts or a collection of nodes bound to a database. A cluster is not part of a database definition and thus does not have a name.
