Find database name. (non-privileged users)

SQL> show user

USER is "SCOTT"

SQL> select ora_database_name from dual;

ORA_DATABASE_NAME
-------------------
NSEDB



SQL> select '&_CONNECT_IDENTIFIER' NAME from dual;
old   1: select '&_CONNECT_IDENTIFIER' NAME from dual
new   1: select 'NSEDB' NAME from dual

NAME
-----
NSEDB