If you are moving the database from one domain to another on the same server, and you want to keep the database name the same, you just need to change the owner of the database in the ‘data_bases’ table in the psa database.
The table uses the field ‘dom_id’ as a reference to the owner. Look in the ‘domains’ table to find the ‘id’ of the domain you are using and the one you wish to move to then make the change in the ‘data_bases” table.
Once changed, you will see the database listed under the new domain in Plesk. You can then add/change usernames and passwords through Plesk as normal.
You can do all the above through the command interface (SSH) or you can do it the easy way with a tool like phpMyAdmin installed.
Source: http://forums.serverbeach.com/showthread.php?t=164