Well, it could be, but that is not necessarily the case. In fact in the sense that “machine.dreamhost.com” is usually taken to refer to your webserver , as in “genki.dreamhost.com”(not your MySQL host), it is generaly not what you will use. the hostname is what you defined as the hostname for the database when you created the database in the control panel. By default, the DH panel suggests “mysql.yourdomain.tld” for the host, and many leave it that way, though you can make it be “mydatastore.yourdomian.tld” or something else if you so desire at database creation time.
This is true, by default, and it is for security reasons, but this does not mean you cannot connect to your database from your home machine, or another machine outside of Dreamhost.
In order to do this you need to modify the permission of the database user you wish to allow to access the database remotely. From the Control Panel–> Goodies --> Manage MySQL screen, click the linked user name for a given database. This will bring up a configuration screen where you can modify that user’s permissions for the database and add additional “hosts” from which that user may access the database. These hosts can be in the form of another domain, or an IP address. Setting these appropriately will allow that user to access the database from that location in addition to from within Dreamhost.