set sqlprompt "_USER'@'_CONNECT_IDENTIFIER SQL>"
below shown code can also be added to get the same output and even run custom query at sqlplus login. As they rely on database tables cannot be used when database is down.
define _editor=vi
set termout off
column prompter new_value m_prompt
select sys_context('USERENV','CURRENT_USER') '@' sys_context('USERENV','DB_NAME')' SQL>' prompter from dual;
set sqlprompt '&m_prompt'
undefine m_prompt
commit;
set termout on