Mirrored site and mysql?

I have a website that is currently hosted with a different company. I am planning on moving the site to my DH account. However, I need to set everything up and make sure it is working before can update the nameserver records to point to the new location at DH. But I don’t know how I can do this without updating the nameserver records, because I need to set up a database and phpBB.

Suppose I have set up the domain ‘domain.com’. I set up a database ‘mydatabase’ and a user for this database. I added a MySQL hostname for this database named ‘mysql.domain.com’. If I need to use the MySQL hostname to connect to the database (i.e. mysql -h mysql.domain.com etc…), then how can I connect to the database when domain.com is still pointing to my old site?