When creating or copying a database from WHM's phpmyadmin, the database map needs to be updated, in order for that new db to show up in the cpanel accounts mysql list.
Create or copy your database with the correct cpanel username structure
"cpaneluser_dbname"
from shell run
/usr/local/cpanel/bin/setupdbmapinfo [setupdbmap] Begin setupdbmapinfo [setupdbmap] Updating MySQLusersinfo [setupdbmap] Processing MySQL databases and databaseusers...Adding database cpaneluser_dbname ownership to cpaneluserSaving MySQL DB mappingforcpaneluser