Can't set root password MySql Server

Hi All -

I have a new droplet with Ubuntu 18.04 and am installing MySql using

sudo apt-get install mysql server

It seems to install fine but does not ask for a root password on install, I am pretty sure this is as it is expected to work.

With this from the cli I can log into it with just using ‘mysql’, while that is handy it is not very secure.

So I stop the services and use

sudo mysql_secure_installation

I go through the steps, set a root password, remove anon users, stop remote root access etc…

Restart the service

I have tried flushing privileges

I can still log in with no password.

I have then tried a couple of other methods that were outlined here, again no luck.

https://www.cyberciti.biz/faq/mysql-change-user-password/

Any thoughts ? What am I forgetting or missing ?

I am beginning to feel real dumb.

Thanks