problem moving to new hosting plan <–and new DB name

I am trying to move my various WP sites from one hosting plan to another. My main reason for doing this is that my current hosting company has a limited amount of MySQL databases I can have (max of 10) and I can’t give the database a descriptive name (the database name is automatically assigned) which makes management a real pain as I have to keep a little table telling me which site is on what database (they name the databases like [domain name]-1, [domain name]-2, etc)

So I have found a new hosting service that has unlimited MySQL databases (that I can assign actual names –and even assign usernames myself). The problem I run into is when I attempt to import the old database to the new one using phpmyadmin. I get an error:

#1044 – Access denied for user ‘[new username]’@’localhost’ to database ‘[old database name]’

I’m guessing the problem is that the username I now have on the newly created database on the new hosting service doesn’t match the old one (not that I want them to). Also, the database name is different too. Now I can easily see I need to change the wp-config.php file to the new database name and username but how can I successfully import the old database if the username and dbname is different?

Thanks in advance guys!