Moving servers with cPanel

Hi all,
I've followed the guidelines on changing servers, (https://www.zen-cart.com/tutorials/index.php?article=100) and been through the faq's and forums but cant find a similar problem.

The 'Old' server has cPanel. When I created the database for the 'Old', site I named it zc1, however cPanel prefixes database names with the first letters of the hosting accocunt, and called it, intellig_zc1.

cPanel is also used as the control panel on the new server. When I install zen and create a new database, I name it zc1 and cPanel renames this db to the new account name prefixed to it, i.e. thestone_zc1.

When I import the 'Old' database with phpmyadmin. It gives errors. i think its because of the name difference in the databases. I've asked the hosting company if they can rename the 'New' database for me, to intellig_zc1, but they are unhelpful.

I wont embarrass myself by telling how many times I've Installed and uninstalled the new site, and started again, trying to figure it out. Any ideas are VERY MUCH appreciated.

Cheers!