I have added several databases from a MySQL dump to my server, however they are not listed under the available databases in Parallels Plesk Panel (PP).
You must have restored the databases manually via mysql command. However, PP does not know anything about them.
In order for the databases to be visible in PP you need to perform the following steps:
1. Delete the manually created databases from MySQL.
2. Log in to the PP control panel and create those databases for the needed domains.
Example for PP 10.x-11.x:
Home -> Subscriptions -> userdomain.com -> Websites & Domains -> Databases -> Add new database
3. Restore the MySQL dump to the newly created databases using mysql command.
After that you will be able to see those databases in PP control panel.