Here is a step-by-step for renaming a table:
1. Log into cPanel
2. Click on "MySQL Databases"
3. On the page that loads, click on the "phpMyAdmin" link at the bottom. This should load a new window.
4. In this new window, select the DB that contains the table you want to modify from the drop down menu at the left (in the darker blue).
5. The screen should refresh with all of the tables in that DB. On the table you want to modify, click the Properties button, which is in the "Action" column, and it's the 4th icon from the left (little blue hand with a piece of paper).
6. At the top of the page now click the blue "Operations" link.
7. On the page that loads, the second item should be "rename table to." Enter the new name and hit "Go" This should rename your table.