You can delete a database created on DreamHost through the panel (Panel > 'Advanced' > 'MySQL Databases').
To the right of the database, click the 'Delete DB' button.
Deleted Databases are moved to the recycle bin. You can access this by clicking the 'MySQL Recycle Bin' button on the top left of the page. This allows for easy restoration of databases that are mistakenly deleted.
Databases are stored here for 30 days. After 30 days, they are permanently deleted.
If you wish to permanently delete a database, you can log into MySQL using the command and issue a "drop database" statement to expedite the process.
What happens to the database user?
If the user for the database you deleted is NOT assigned to any other database, it will also be deleted along with the database.