I had this problem on a fresh install on Mac. I installed MariaDB with:
brew install mariadb
Then started the service:
brew services start mariadb
I was unable to run 'mysql_secure_installation' as it prompted for the root password. Then I noticed in the install output:
mysql_install_db --verbose --user=jonny --basedir=/usr/local/Cellar/ ....
So I tried logging in as the username specified in the mysql_install_db output and was successful e.g.
mysql -u jonny
Then at the mysql prompt if you want to set a password for the root user:
SET PASSWORD FOR 'root'@'localhost' = PASSWORD('ToPsEcReT');