A new comer to Joomla and mySql atmosphere. Produced a Joomla test atmosphere on localhost but didn't title the mySql database to that particular from the target Web service provider. It is possible to method to relabel the database in order to load to Web service provider?

Presuming I understood your question and also you really installed joomla on localhost but would now like to move it and it is data for your web service provider hosting environement, you've two places where you have to alter the db title (presuming joomla 1.5.6/latest):

JOOMLA_DIR\configuration.php
$db = 'your-db-name'

JOOMLA_DIR\LIBRARIES\JOOMLA\config.php
$db = 'your-db-name'

In case your information is important, remember to create a backup first.