Update:
I re-installed the mariadb docker without password and then I managed to login with root account (no password) - then manually changed the password
mysql -u root -p
mysql> use mysql;
mysql> update user set password=PASSWORD("NEWPASSWORD") where User='root';
mysql> flush privileges;
mysql> quit
and I managed to login again with new password (both from docker instance and remotely from my windows machine) - Then I restarted the mariadb docker and then I can see it cannot start properly and in a endless loop
[cont-init.d] 10-adduser: executing...
usermod: no changes
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GID/UID
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User uid: 99
User gid: 100
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[cont-init.d] 10-adduser: exited 0.
[cont-init.d] 30_config: executing...
[cont-init.d] 30_config: exited 0.
[cont-init.d] 40-initialise-db: executing...
[cont-init.d] 40-initialise-db: exited 0.
[cont-init.d] done.
[services.d] starting services
[services.d] done.
170906 08:38:30 mysqld_safe Logging to syslog.
170906 08:38:30 mysqld_safe Starting mysqld daemon with databases from /config/databases
170906 08:38:34 mysqld_safe Logging to syslog.
170906 08:38:34 mysqld_safe Starting mysqld daemon with databases from /config/databases
170906 08:38:37 mysqld_safe Logging to syslog.
170906 08:38:37 mysqld_safe Starting mysqld daemon with databases from /config/databases
170906 08:38:40 mysqld_safe Logging to syslog.
170906 08:38:40 mysqld_safe Starting mysqld daemon with databases from /config/databases
170906 08:38:44 mysqld_safe Logging to syslog.
170906 08:38:44 mysqld_safe Starting mysqld daemon with databases from /config/databases
170906 08:38:47 mysqld_safe Logging to syslog.
170906 08:38:47 mysqld_safe Starting mysqld daemon with databases from /config/databases
170906 08:38:50 mysqld_safe Logging to syslog.
Also not from the docker instance itself
root@2262d249c970:/# mysql -u root -p
Enter password:
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock'