Mysql host?

I’m setting up a mysql database, and it appears that my only option to create one is to set up a subdomain strictly for mysql. Let’s say I have 10 clients and they all have their own domain using my server, but the databases I have set up for them are all on one server. Can’t I just set up ONE big mysql server and put a bunch of databases in them, or with Dreamhost do I have to create seperate subdomains for every database that I want? Hope I made sense with this.

each database has to have its own subdomain - we need to be able to reassign databases to a new machine or MySQL instance easily, which requires some flexibility with changing the DNS in order to make the move fairly transparent.

you can easily create one database, though (with one subdomain), and create lots of tables within that database.