No More Root

Firstly, change the root account to some other name - it's in the "users" section of Phpmyadmin ("priviledges" on some older versions).

Move PhpMyadmin to a less obvious location

Secondly, move phpmyadmin to another address.

You can do this by editing the apache configuration file for Phpmyadmin.

On (for example) an Ubuntu Linux server, the file is /etc/phpmyadmin/apache.conf .

Right near the top of the file you'll see: Alias /phpmyadmin /usr/share/phpmyadmin

Change the first phpmyadmin (only) to something else (but not the same not this example): Alias /lessobvious /usr/share/phpmyadmin

Save it, and restart apache.

Now., you can reach phpmyadmin on your server with:

http://www.example.com/lessobvious/

And it won't be too easy to find for somebody doing a brute force attack to login.