trigger on AFTER LOGON DATABASE

[oracle newbie]

I found one coding on site and i have 2 doubt
The DATABASE is refering to all the database ?
Can I change the word to a Connection Name?

create or replace trigger
logon_audit_trigger
AFTER LOGON ON DATABASE
BEGIN
insert into stats$user_log values(
user,
sys_context('USERENV','SESSIONID'),
sys_context('USERENV','HOST'),
null,
null,
null,
sysdate,
to_char(sysdate, 'hh24:mi:ss'),
null,
null,
null
);
END;

[debasisdas]

in your sample code the term DATABASE referes to the database in which the Trigger exists.

So no need to specify the name.