SET SQL PROMPT TO DATABASE NAME

spool set_prompt.sql
select 'set sqlprompt '||value||'>'
from sys.v$parameter where name='db_name';
spool off
start set_prompt.sql

The content of the resulting script, SET_PROMPT.SQL, will look like this:
set sqlprompt V715>
and when run the command will change your prompt from the default
SQL>
to
V715>