The left side of the main screen of phpMyAdmin is where you will find your database listed, with the table listed below the database name. The right side, a big white screen is where the actions take place. To start, select the database table you wish to rename in the list on the left hand side window. Select the table by clicking on it. The window on the right hand side will open up with the details about the table you have selected. Now, at the top of the right hand screen, click on the Operations button. This will open a list of actions you can perform on the table you have selected.
Scroll down to the box titled "Table Options". The first line is Rename table to with an empty box. Enter the new name for your table in this box. When you are done, click on the Go Button in the lower right corner. This will open the confirmation window, which shows that the table has been renamed. If you look in the panel on the left hand side, the table you selected is now showing the new name.