DirectAdmin doesn't store any of its data in mysql. Also, the database names themselves are queried each time, to assemble a user's database list. All done realtime, no lists of databases stored anywhere.
I use phpMyAdmin for some stuff, but mainly I just use "mysql" itself from the command line to do work. I think I heard reference of programs that can be used on a local machine that connect to the server (Hence the access hosts feature).. although, I havn't used them myself, they seem like a good idea.
John