How to proper setting root mysql password
I got the problem, basically almost all the solution you can find around are outdated.
With mysql 8.0.15 you have to follow this guide
https://dev.mysql.com/doc/refman/8.0/en/resetting-permissions.html

I recommend to read the whole page, but basically you have to use  

ALTER USER 'root'@'localhost' IDENTIFIED BY 'MyNewPass';


NOTE Using the method UPDATE mysql.user SET authentication_string.. will lock you out from your own mysql server (you won't solve even with mysqld_safe --skip-grant-tables).
If you end up locked out, I guess the only hope (I didn't test it) is to stop mysqld and relaunch mysqld manually using --init-file="myinitfile" where myinitfile is a plain text file containing the ALTER USER instruction I mentioned before (I'm not sure it is even doable if you have installed mysql using brew, but note I'm new to macOS). Mine was a fresh installation, so I've just deleted the whole /usr/local/var/mysql directory and reinstalled mysql.