[eluser]TheFuzzy0ne[/eluser]
They have intentionally allowed you to only create databases through their UI, because they have their own structure which they need to enforce. They might need to keep track of how many databases you have created, and also prefix database names with a unique string to prevent naming collisions with the other 999 accounts on the server.
The only way to get around that, is to prefix tables with a unique string to allow them to reside in the same database, or to design your database to allow for single tables, and you instead pull data out using a customer ID, rather than customer specific databases/tables.
However, whatever it is you're trying to do, it would seem that this particular host (or maybe even shared hosts in general), is not suitable for your situation.