Here are the step by step instructions for renaming a table in phpMyAdmin:
1) Log into cPanel
2) Click on the phpMyAdmin link at the bottom
3) In phpMyAdmin screen select the database that contains the table you want to modify. Tables in selected database will be listed.
4) Click the table you want to modify.
5) Click the Operations link at the top of the page
6) In the Table options, there is the field "Rename table to"
7) Enter new table name and click Go.
8) It's done. Following these steps, your MySQL table should now be renamed.