Admin password of MariaDb doesn't seem to work
That behaviour sounds consistent with enabling the plugin for socket authentication for the root user, where MariaDB trusts operating system credentials received over the socket and does not rely on a password. By using
sudo or logging on as root you can connect to the database server as root, because you're root on the OS, but other OS users can't.
You can remove that option with:
$ sudo mysql -u root mysql> use mysql; mysql> update user set plugin='' where User='root'; mysql> flush privileges;
and then you get the expected behaviour any user that has the MariaDB root password should be able to log on as root.
The alternative is to set up another user, not root, that also has full administrator privileges and use that, rather than root, for admin purposes:
$ sudo mysql -u root mysql> CREATE USER 'finley'@'localhost' IDENTIFIED BY 'some_pass'; mysql> GRANT ALL PRIVILEGES ON *.* TO 'finley'@'localhost' -> WITH GRANT OPTION;