PostgreSQL, what is the hostname address of my default database?
If you're connecting from the same machine, use localhost

A given computer can run multiple instances of PostgreSQL on different sockets (address:port pairs). The default port is 5432

A given PostgreSQL server can run multiple databases on the same instance. The postgres database is always there. There's no "default database" though really.

Are you sure the service is enabled and running? Did you set listen_addresses in postgresql.conf and set up authentication in pg_hba.conf?

Is the service actually running?