Renaming database may cause scripts to be failed. So, in case of renaming database, be sure that configuration files of scripts that reference this database are updated. Also you need to reconfigure User Permissions.
To rename database, follow below steps:
1- Login to your cPanel account and click on MySQL Databases.
2- Scroll down to reach Current databases section. In this section you can see list of your all databases.
3- Choose the database that you want to change its name, and then click on Rename button.
4- In the opening window, enter new database name to rename database.
5- Click the Proceed button to finish database renaming operation.