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/setupdbmap

info [setupdbmap] Begin setupdbmap
info [setupdbmap] Updating MySQL users
info [setupdbmap] Processing MySQL databases and database users ...
        Adding database cpaneluser_dbname ownership to cpaneluser
        Saving MySQL DB mapping for cpaneluser