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