Figure out what username you use to start your odoo server. Check out the logs. It should be the owner of your database.

I know it's an old topic, but I still have the same problem on the current odoo 17.

I'm running a dedicated postgres server and created one database there for odoo. I have set the connections to the server in the odoo.conf file

db_host = postgresql.my.domain

db_port = 5432

db_user = odoo_cc

db_password = MyPasswd

addons_path = /usr/lib/python3/dist-packages/odoo/addons

db_name = odoo_demo

Obviously it is failing with the error message, that there is access to the "posthres" database.

failed: FATAL:  no pg_hba.conf entry for host "192.168.33.40", user "odoo_cc", database "postgres", no encryption

How do I need to configure odoo, if I want to fix it to one single database and what steps do I need to apply to initialize that database (if that is even necessary).

Since I'm currently experimenting with odoo, I'm still on the community edition, but planning to change to enterprise soon. I just want to have it under my own control.

Thanks for the suggestion, but I don't think that is the issue. 

The database user name is correct (as tested using psql -U odoo -W odoo -h 10.0.1.10)

The probelm from the logs is thaty odoo is trying to connect to the database named "postgres", which it does not and should not have permission to.  It is ignoring the directive to connect to db_name = odoo

My database server runs a database for a number of different programs and they should be segregated, connecting to the "postgres" database allows changing of usernames and passwords, not a good move for security.

Perhaps on first run, odoo is trying to create a database and wanting to access the user table?  However, I have already created a database.