The v$ tables contain meta information:

select * from v$database;

gets you some basic information (which includes the database name, IIRC).

update (2008-12-22):

Since we seem to be reviving this thread - here is another one:

select ora_database_name from dual

(Oracle 10g)

In reply to Re: [OT] Get the database name in Oracle by erix
in thread [OT] Get the database name in Oracle by kulls

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